Question

Karla is riding vertically in a hot air balloon, directly over a point P on the ground. Karla spots a parked car on the ground at an angle of depression of 30o. The balloon rises 50 meters. Now the angle of depression to the car is 35°. How far is the car from point P?

Answer 1

We form 2 similar rt. triangles:

Triangle #1.
X = Hor. side = dist. from P to the car.
Yi = Ver. side.
A = 30o.

Triangle #2.
X = Hor. side = Dist. from P to the car.
Y2 = Y1+50 = Ver. side.
A = 35o.

Use aw of Sines.
sin30/Y1 = sin35/(Y1+50).
Cross multiply:
(Y1+50)sin30 = Y1*sin35
Y1/2+25 = 0.574Y1
Multiply both sides by 2:
Y1+50 = 1.148Y1
1.148Y1-Y1 = 50
0.148Y1 = 50
Y1 = 337.8 m.

tan30 = Y1/X = 337.8/X
X = 337.8/tan30 = 585 m.

Answer 2

714 feet away

Answer 3

I gave up.

Answer 4

234.97

Answer 5

this is just common sense. How can the angle of depression be higher when karla rises. If she is rising, it is physically impossible for the angle of depression to go higher. This question isnt worded right.

Answer 6

I read the first word and gave up 🤣

Answer 7

The hot air balloon has an angle of depression of 36° to the point of the ground. The distance between the hot air balloon and the ground is 75 ft.