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# Trigonometry Word problem

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Two planes leave Dawson City Airport at the same time. One airplane travels 420 km/hour. The other airplane travels at 375 km/hour. Two hours later they are 1500km apart.

Algebraically determine the angle between their paths, rounded to the nearest degree.

Jul 27, 2021

#1
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Draw a triangle.

Dawsen city aiport is at one vertice

in 2 hours how far does each plane fly?  Those distances are on the two sides radiating from Dawson city

The other side is 1500km

Use cosine rule to find the angle.

Jul 27, 2021
#2
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In two hours, one airplane has traveled 840 km and the other 750 km.

By the cos rule, we have $1500^2 = 840^2 + 750^2 - 2(750)(840) \cos \gamma$

$981900 = - 2(750)(840) \cos \gamma$

$\cos \gamma = 0.77928571428$

$\gamma = \cos ^{-1} 0.77928571428$

$\gamma = 38.739424597856$

$\gamma = \boxed{39^{\circ}}$

Jul 27, 2021
#3
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