Posted by **Bianca** on Tuesday, June 1, 2010 at 2:10am.

Two men on the same side of a tall building notice the angle of elevation to the top of the building to be 30o and 60o respectively. If the height of the building is known to be h =120 m, find the distance (in meters) between the two men.

- trig -
**MathMate**, Tuesday, June 1, 2010 at 8:23am
Assuming that both observers are at an elevation level with the base of the building.

Height of the building, H = 120m

Distance of observer 1 = D1

Angle of elevation = α

By the definition of tangent = opp/adj

H/D1=tan(α), therefore

D1=H/tan(α)

Since H and α are known, D1 can be calculated numerically.

Distance of observer 2 = D2

Angle of elevation = β

H/D2=tan(β)

D2=H/tan(β)

Distance between observers = D2-D1

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