A 50 ft tall tree is casting a shadow while the sun is at an angle of elevation of 63 . to the nearest foot, how long is the tree's shadow?

Remark

The question is an application of the Tangent Function.

Tan (63) = Opposite / Adjacent

Givens

Opposite side = height of the tree = 50 feet.

Adjacent side = shadow length which we have to solve for.

Solution

Tan (63) = opposite / Adjacent Add a 1 on the left so you have a proportion.

Tan (63) / 1 = 60 / adjacent Cross multiply

Adjacent * Tan (63) = 1 * 60

Adjacent = 60 / tan (63)

Adjacent = 60 / 1.963

Adjacent = 30.57 feet.