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?

the height of the helicopter is 126.82 feets

Step-by-step 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

yes. we do proportions in probabilities.

answer: what are the following choices