Question

from a balloon vertically above a straight road the angle of depression of two cars is 45 degree and 60degree if the cars are 100 m apart then find the height if balloon

Answer 1

Let's say that the balloon is at a height 'h'

Car 1 is at the depression angle of 45 degrees.
Car 2 is at the depression angle of 60 degrees.

When you make the diagram, you will notice that Car 2 is between the Balloon and Car 1.

From the point below the balloon, let's say point P, we will measure the distance of the cars.

From P to Car 2, the distance (D2) we can find as

tan(90-60) = (D2/h)

tan(30) = (D2/h)

(1/✓3) = (D2/h)

D2 = (h/✓3)

From P to Car 1, the distance (D1) we can find as

tan(90-45) = (D1/h)

tan(45) = (D1/h)

1 = (D1/h)

D1 = h

Now we know that the distance between the two cars is 100m.

D1 - D2 = 100

h - (h/✓3) = 100

h×(1 - (1/✓3)) = 100

h×((✓3 - 1)/√3) = 100

h = (100✓3)/(✓3 - 1)

h = 236.6025403784 m

Hence the Balloon is approximately at a height of 236.6 m