Pre-Calc/Trig Unit 3: Analytic Trig and Applications/7.5 Apps of Vectors Airspeed of aircraft A pilot wants to fly on a bearing of «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mo»§#160;«/mo»«mo»§#176;«/mo»«/math». By flying due east, he finds that a #b -mph wind, blowing from the south, puts him on course. Find the airspeed of the plane, rounded to the nearest mph.

]]> 1.0000000 0.3333333 0 0 #answer]]> Great!

]]> 1.0000000 0.3333333 0 0 #answer]]> Awesome!

]]> <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>615</mn><mo>,</mo><mn>630</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>160</mn><mo>,</mo><mn>180</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>arccos</mi><mo>(</mo><mfrac><mrow><msup><mn>691</mn><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><msup><mi>b</mi><mn>2</mn></msup></mrow><mrow><mo>-</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>b</mi></mrow></mfrac><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>convert</mi><mo>(</mo><mi>c</mi><mo>,</mo><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><mn>180</mn><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>-</mo><mi>d</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>615</mn><mo>,</mo><mn>630</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>617</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>160</mn><mo>,</mo><mn>180</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>160</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>arccos</mi><mo>(</mo><mfrac><mrow><msup><mn>691</mn><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><msup><mi>b</mi><mn>2</mn></msup></mrow><mrow><mo>-</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>b</mi></mrow></mfrac><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1.9397</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>convert</mi><mo>(</mo><mi>c</mi><mo>,</mo><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>111.14</mn><mo> </mo><csymbol definitionURL="http://.../units/degree/angular">°</csymbol></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><mn>180</mn><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>-</mo><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>68.864</mn><mo> </mo><csymbol definitionURL="http://.../units/degree/angular">°</csymbol></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></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><correctAnswer id="2"></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><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-1)</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"/></localData></question> Angle rope makes with vertical (needs more work) A box weighing #a lb is hanging from the end of a rope. The box is pulled sideways by a horizontal rope with a force of #b lb. What angle, to the nearest degree, does the first rope make with the vertical?

]]> 1.0000000 0.3333333 0 0 #answer]]> Great job!!

]]> 1.0000000 0.3333333 0 0 East component=#eNorth component=#n]]> Great job!!

]]> Did you recognize it was a 45-45-90 right triangle?

]]> Solve the problem.A box weighing 80 lb is hanging from the end of a rope. ... Solve the problem.

A box weighing 80 lb is hanging from the end of a rope. The box is pulled sideways by a horizontal rope with a force of 24 lb. What angle, to the nearest degree, does the first rope make with the vertical?]]> 1.0000000 0.3333333 0 0 17° * Solve the problem.A fishing boat leaves port on a bearing of 35° and travels ... Solve the problem.

A fishing boat leaves port on a bearing of 35° and travels 13.3 mi. The boat then turns due east and travels

How far is the fishing boat from port, and what is its bearing from port?]]> 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 1.0000000 0.3333333 0 true true abc 11.5 mi; 46.9° Incorrect 15.9 mi; 46.9° Correct 10.3 mi; 11.9° Incorrect 15.9 mi; 11.9° Incorrect Solve the problem.A hot-air balloon is rising vertically 12 ft/sec while the ... Solve the problem.

A hot-air balloon is rising vertically 12 ft/sec while the wind is blowing horizontally at 5 ft/sec. Find the angle that the balloon makes with the horizontal.]]> 1.0000000 0.3333333 0 0 67.4° * Solve the problem.A plane is heading due south with an airspeed of 264 mph. ... Solve the problem.

A plane is heading due south with an airspeed of 264 mph. A wind from a direction of 59° is blowing at 13 mph. Find the bearing of the plane.]]> 1.0000000 0.3333333 0 0 182° * Solve the problem.A ship leaves point A and travels directly north to point ... Solve the problem.

A ship leaves point A and travels directly north to point B. From point B, the ship then travels due east to point C. The magnitude of the vector from point A to point C is 134. Find the magnitude of the northern vector. Find the magnitude of the eastern vector.]]> 1.0000000 0.3333333 0 true true abc north; 67

east]]> 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 Correct east]]> 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 Incorrect 67 north; 67 east Incorrect north; 67 east]]> 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 Incorrect Solve the problem.Two people are carrying a box. One person exerts a force ... Solve the problem.

Two people are carrying a box. One person exerts a force of 135 pounds at an angle of 47.7° with the horizontal. The other person exerts a force of 95 pounds at an angle of 50.9°. Find the weight of the box.]]> 1.0000000 0.3333333 0 0 176 lb * Solve the problem.What is the minimum force required to prevent a ball ... Solve the problem.

What is the minimum force required to prevent a ball weighing 26.7 lb from rolling down a ramp inclined 32.3° with the horizontal?]]> 1.0000000 0.3333333 0 0 14.3 lb * Weight of boat being pulled up ramp A force of #a lb is required to pull a boat up a ramp inclined at 18° with the horizontal. How much does the boat weigh? Round to the nearest pound.

]]> 1.0000000 0.3333333 0 0 #answer]]> Nice work!