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 25°. 

As her balloon ride continues, she rises 50m and sees the car again, now the angle of depression to the car is 30°. How far is the car from point P?  

in Trigonometry Answers by Level 1 User (360 points)

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1 Answer

Let distance of the car from p be x. And initial height be y.

So, y/x=tan25   --------------------(1)

And After ascending 50 metres

(y + 50)/x = tan30  ----------------------(2)

Dividing (2)  by (1) we get

(y+50)/y = tan30/tan25

=> (y+50)/y = 1.2381316478

=>y + 50 = 1.238131 y

=> 1.238131 y - y = 50

=> y = 50/0.238131

=> y = 209.967891

Therefore, x = y/tan25  ------ from (1)

So, x = 450.277596 m

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