Pre-Calc/Trig Unit 3: Analytic Trig and Applications/7.3 Law of Cosines and Heron's Formula
Cans of paint needed
A painter needs to cover a triangular region #a meters by #b meters by 73 meters. A can of paint covers 70 square meters. How many cans will be needed? (When rounding, consider how many can will need to be purchased to get the job done).]]>
Use Heron's Formula to find the area of the triangle needing paint.]]>
1.0000000
0.3333333
0
0
#answer]]>
<question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>65</mn><mo>,</mo><mn>70</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>60</mn><mo>,</mo><mn>66</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>*</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mn>73</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><msqrt><mrow><mi>s</mi><mo>*</mo><mo>(</mo><mi>s</mi><mo>-</mo><mi>a</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>s</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>s</mi><mo>-</mo><mn>73</mn><mo>)</mo></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><mfenced close="⌉" open="⌈"><mfrac><mi>t</mi><mn>70</mn></mfrac></mfenced></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>ns</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m, y, z, a, f, p, n, µ, d, da, h, G, T, P, E, Z, Y</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-0)</option><option name="precision">4</option><option name="relative_tolerance">false</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession">null</data></localData></question>
Cost to carpet room
A room in the shape of a triangle has sides of length 10.0 yards, #a yards, and #b yards. If carpeting costs $13.90 per square yard, padding costs $ #c per square yard, and there is no charge for installation, how much, to the nearest dollar, will it cost to carpet the room? (Round area up next integer before applying cost).]]>
Use Heron's Formula to find the required area.]]>
1.0000000
0.3333333
0
0
#answer]]>
<question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>9</mn><mo>,</mo><mn>13</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>12</mn><mo>,</mo><mn>17</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>.</mo><mn>25</mn><mo>,</mo><mn>1</mn><mo>.</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>*</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><msqrt><mrow><mi>s</mi><mo>*</mo><mo>(</mo><mi>s</mi><mo>-</mo><mi>a</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>s</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>s</mi><mo>-</mo><mn>10</mn><mo>)</mo></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><mfenced close="⌉" open="⌈"><mi>t</mi></mfenced><mo>*</mo><mo>(</mo><mn>13</mn><mo>.</mo><mn>9</mn><mo>+</mo><mi>c</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>ns</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m, y, z, a, f, p, n, µ, d, da, h, G, T, P, E, Z, Y</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-0)</option><option name="precision">3</option><option name="relative_tolerance">false</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession">null</data></localData></question>
Distance between Two Towns
To find the distance between 2 small towns, and electronic distance measuring (EDM) instrument is placed on a hill from which both towns are visible. If the distance from the EDM to the towns is #a miles and #b miles and the angle between the two lines of sight is 70o, what is the distance between the two towns? (Round answer to nearest tenth of a mile.)]]>
Draw a diagram. Law of Cosines.]]>
1.0000000
0.3333333
0
0
#answer]]>
<question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>4</mn><mo>.</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>3</mn><mo>.</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><msqrt><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mn>70</mn><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>)</mo></mrow></msqrt></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>n</mi><mi>s</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-1)</option><option name="relative_tolerance">false</option><option name="precision">2</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession">null</data></localData></question>
Find area using Heron's Formula
Find the area of triangle ABC with the given parts. Round to the nearest whole number.
a = #a cm
b = 15.0 cm
c = 13.0 cm]]>
Heron's Formula]]>
1.0000000
0.3333333
0
0
#answer]]>
<question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>15</mn><mo>,</mo><mn>22</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>(</mo><mi>a</mi><mo>+</mo><mn>15</mn><mo>+</mo><mn>13</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><msqrt><mrow><mi>s</mi><mo>*</mo><mo>(</mo><mi>s</mi><mo>-</mo><mi>a</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>s</mi><mo>-</mo><mn>15</mn><mo>)</mo><mo>*</mo><mo>(</mo><mi>s</mi><mo>-</mo><mn>13</mn><mo>)</mo></mrow></msqrt></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>ns</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m, y, z, a, f, p, n, µ, d, da, h, G, T, P, E, Z, Y</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-0)</option><option name="relative_tolerance">false</option><option name="precision">2</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession">null</data></localData></question>
Find the indicated angle or side.Find the length of side a.
Find the indicated angle or side.
Find the length of side a.
]]>
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
1.0000000
0.3333333
0
0
7
*
Find the indicated angle or side.Find the measure of angle A.
Find the indicated angle or side.
Find the measure of angle A.
]]>
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
1.0000000
0.3333333
0
0
120°
*
Find the missing parts of the triangle. (Find angles to the nearest ...
Find the missing parts of the triangle. (Find angles to the nearest hundredth of a degree.)
a = 6.1 in.
b = 13.6 in.
c = 16.0 in.]]>
1.0000000
0.3333333
0
true
true
abc
A = 21.92°, B = 56.34°, C = 101.74°
Correct
A = 19.92°, B = 56.34°, C = 103.74°
Incorrect
A = 23.92°, B = 54.34°, C = 101.74°
Incorrect
No triangle satisfies the given conditions.
Incorrect
Find the missing parts of the triangle.B = 63°30'a = 12.20 ftc = 7.80 ft
Find the missing parts of the triangle.
B = 63°30'
a = 12.20 ft
c = 7.80 ft]]>
1.0000000
0.3333333
0
true
true
abc
No triangle satisfies the given conditions.
Incorrect
b = 11.17 ft, A = 77°49', C = 38°41'
Correct
b = 13.17 ft, A = 73°07', C = 37°23'
Incorrect
b = 12.17 ft, A = 75°07', C = 41°23'
Incorrect
Two planes leave airport at same time
Two airplanes leave an airport at the same time, one going northwest (bearing 315°) at #a mph and the other going east at #b mph. How far apart are the planes after #c hours (to the nearest mile)?]]>
Draw a diagram. Find distance each plane travels, then use Law of Cosines]]>
1.0000000
0.3333333
0
0
#answer]]>
<question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>400</mn><mo>,</mo><mn>430</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>330</mn><mo>,</mo><mn>340</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><msqrt><mrow><mo>(</mo><mi>a</mi><mo>*</mo><mi>c</mi><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mo>(</mo><mi>b</mi><mo>*</mo><mi>c</mi><msup><mo>)</mo><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><msup><mi>c</mi><mn>2</mn></msup><mo>*</mo><mi>cos</mi><mo>(</mo><mn>135</mn><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>)</mo></mrow></msqrt><mo>*</mo><mn>1</mn><mo>.</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>ns</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m, y, z, a, f, p, n, µ, d, da, h, G, T, P, E, Z, Y</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-0)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession">null</data></localData></question>
Two ships leave port at same time
Two ships leave a harbor together traveling on courses that have an angle of #a ° between them. If they each travel #b miles, how far apart are they (to the nearest mile)?]]>
Draw a diagram. Law of Cosines.]]>
1.0000000
0.3333333
0
0
#answer]]>
<question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>110</mn><mo>,</mo><mn>130</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>480</mn><mo>,</mo><mn>540</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><msqrt><mrow><mo>(</mo><mi>b</mi><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mo>(</mo><mi>b</mi><msup><mo>)</mo><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>b</mi><mo>*</mo><mi>b</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>a</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>)</mo></mrow></msqrt><mo>*</mo><mn>1</mn><mo>.</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>ns</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m, y, z, a, f, p, n, µ, d, da, h, G, T, P, E, Z, Y</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-0)</option><option name="relative_tolerance">false</option><option name="precision">3</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession">null</data></localData></question>