Trigonometry-15

Two men standing on opposite sides of a flag staff measures the angles of elevation of the top

of the flag staff as 30⁰ and 60⁰. If the height of the flag staff is 20 m, find the distance between the men.

Solution: Let CD be the flag staff. A and B are the places where the two men are standing.

CD = 20 m

∠CAD = 30⁰

∠CBD = 60⁰

Now CD / AC = tan 30⁰

CD = AC x 1/√3

Therefore, AC = CD x √3 = 20 √3 m

CD / CB = tan 60⁰ ; Therefore, CB = CD / tan 60⁰ = 20 / √3 m

AC + CB = (20 √3 + 20/√3) m = 20 (√3 + 1/√3) = 20(3 + 1)/√3 m

i.e. AB = 80 / √3 = 80 / √3 X (√3/ √3) = 80 √3 / 3

The distance between the men = 80 X 1.732 / 3 = 46.19 m (approximately)