Question

. from a balloon, the angle of depression of a ground marker is 27.8 o . from a point 345 m higher, the angle of depression is 46.2 o . find the height of the balloon.

Answer 1

Let φ = 90 - θ where φ is measured from the ground

φ1 = 90 - 27.8 = 62.2

φ2 = 90 - 46.2 = 43.8

L / H1 = tan 62.2 or L = H1 * 1.90

L / (H1 + 345) = tan 43.8 or L = (H1 + 345) * .959

1.90 * H1 = .959 H1 + 331

.94 H1 = 331

H1 = 352

H (height of balloon) = 352 + 345 = 697 m