Question

Two observors on the groundsimutaneously measure

the angle of elevation to a
helicopter. One angle ismeasured as 30degree and
the other as45degree. If the observors are200
feet apart and the helicopterlies over the line
joining them, how high is thehelicopter?

Answer 1

Answer: the height of the helicopter is 126.82 feets

Explanation:

The attached photo represents the scenario. Triangle ABC is formed. Triangles ACD and BCD are right angle triangles.

AD = x feet

BD = (200 - x) feet

h represents the height of the helicopter.

Applying trigonometric ratio,

Tan# = opposite side/ adjacent side.

Considering triangle ACD,

Tan 30 = h/x

h = xtan30 = 0.5774x

Considering triangle BCD,

Tan 45 = h/(200 - x)

h = (200 - x) × tan 45

h = 200 - x

Therefore,

0.5774x = 200 - x

0.577x + x = 200

1.577x = 200

x = 200/1.577 = 126.82 feets