Question

Todd's friend Olivia is flying her stunt plane at an elevation of 6.3 km. From the ground, Todd sees the plane moving directly toward him from the west at a 49° angle of elevation. Three minutes later he turns and sees the plane moving away from him to the east at a 65° angle of elevation. How fast is Olivia flying in kilometers per hou

Answer 1

So the plane of Olivia travels from west to east with an elevation of 6.3 km. To summarize everything and to get the speed of the plane, I used the Angle Side Angle Triangle Theorem and also the law of sine and the formula would be the following:

First is to get the distance traveled by the plane within the range of 3 minutes. To get that distance you must get the following variable.

total distance = distance travel from west to Todds position + distance traveled from Todds position to the reach of the elevation

Dt = D1 + D2

first is getting the D1

D1 = sin41 (6.3) / sin 49
(by following the law of sine and the angles is based on the triangle)
D1 = 5.477 km

then get D2,
D2 = 6.3 sin 65 / sin 25
D2 = 13.510

After that get the total distance

Dt = D1 + D2
Dt = 18.987 km

To get the speed of the plane, you must divide the distance to the time (in minutes) then multiply it by 60 to make it as an hour.

Speed = 18.987 /3 * 60 = 379.74 km/hr