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.
(please solve using trigonometry)
+118667 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.
+876 In two hours, one airplane has traveled 840 km and the other 750 km.
By the cos rule, we have $1500^2 = 840^2 + 750^2 - 2(750)(840) \cos \gamma$
$981900 = - 2(750)(840) \cos \gamma$
$\cos \gamma = 0.77928571428$
$\gamma = \cos ^{-1} 0.77928571428$
$\gamma = 38.739424597856$
$\gamma = \boxed{39^{\circ}}$
