Pre-Calc/Trig Unit 1: Trig Functions/2.4 Solving Right Triangles
Find distance to ranger station (Angle of Depression)
From a balloon 900 feet high, the angle of depression to the ranger headquarters is «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mo»§#160;«/mo»«mo»§#176;«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mo»`«/mo»«/math». How far is the headquarters from a point on the ground directly below the balloon (to the nearest foot)?]]>
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>50</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>5</mn><mo>,</mo><mn>55</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><mfrac><mn>900</mn><mrow><mi>tan</mi><mo> </mo><mo>(</mo><mi>a</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mi>b</mi><csymbol definitionURL="http://.../units/minute/angular">'</csymbol><mo>)</mo></mrow></mfrac></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>
Find distance to tower (Angle of Depression)
From the top of a vertical tower, #a feet above the the surface of the earth, the angle of depression to a doghouse is «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mn»61«/mn»«mo»§#176;«/mo»«/msup»«mn»45«/mn»«mo»`«/mo»«/math». How far is it from the doghouse to the foot of the tower? Round your answer to the hundredths place.]]>
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>320</mn><mo>,</mo><mn>340</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><mfrac><mi>a</mi><mrow><mi>tan</mi><mo>(</mo><mn>61</mn><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mn>45</mn><csymbol definitionURL="http://.../units/minute/angular">'</csymbol><mo>)</mo></mrow></mfrac></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">m, s, g</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><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">false</option><option name="precision">5</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 height of building (Angle of Elevation)
A contractor needs to know the height of a building to estimate the cost of a job. From a point #a ft from the base of the building, the angle of elevation to the top of the building is found to be 40°46'. Find the height of the building. Round your answer to the hundredths place.]]>
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>75</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>tan</mi><mo>(</mo><mn>40</mn><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mn>46</mn><csymbol definitionURL="http://.../units/minute/angular">'</csymbol><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^(-2)</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>
Find height of cliff (Angle of Elevation)
From a boat on a lake, the angle of elevation to the top of a cliff is «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mo»§#160;«/mo»«mo»§#176;«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#160;«/mo»«mo»`«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»c«/mi»«mo»§#160;«/mo»«mo»``«/mo»«/math». If the base of the cliff is 655 feet from the boat, how high is the cliff (to the nearest foot)?]]>
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>25</mn><mo>,</mo><mn>35</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>10</mn><mo>,</mo><mn>50</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>5</mn><mo>,</mo><mn>55</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><mn>655</mn><mo>*</mo><mi>tan</mi><mo>(</mo><mi>a</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mi>b</mi><csymbol definitionURL="http://.../units/minute/angular">'</csymbol><mi>c</mi><csymbol definitionURL="http://.../units/second/angular">''</csymbol><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>
Find length of shadow (Pythagorean Theorem)
On a sunny day, a tree and its shadow form the sides of a right triangle. If the hypotenuse is 35 meters long and the tree is #a meters tall, how long is the shadow? Round to the nearest meter.]]>
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>25</mn><mo>,</mo><mn>30</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><mn>35</mn><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></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></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>
Solve the right triangle. If two sides are given, give angles in degrees ...
Solve the right triangle. If two sides are given, give angles in degrees and minutes.
A = 18° 19', c = 276 ft
Round side lengths to two decimal places.]]>
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
1.0000000
0.3333333
0
true
true
abc
B = 71° 41'; a = 86.74 ft; b = 262.02 ft
Correct
B = 71° 40'; a = 89.94 ft; b = 263.22 ft
Incorrect
B = 71° 41'; a = 86.17 ft ; b = 261.13 ft
Incorrect
B = 72° 40'; a = 86.74 ft; b = 258.02 ft
Incorrect
Solve the right triangle.B = 42.1°, c = 4.2 mm, C = 90°
Solve the right triangle.
B = 42.1°, c = 4.2 mm, C = 90°]]>
1.0000000
0.3333333
0
true
true
abc
a = 3.1 mm, A = 47.9°, b = 2.8 mm
Correct
a = 2.8 mm, A = 47.9°, b = 3.1 mm
Incorrect
a = 2.3 mm, A = 47.9°, b = 3.5 mm
Incorrect
a = 3.1 mm, A = 47.9°, b = 2.3 mm
Incorrect