Question

7) Find the height of a pine tree thatcasts a 41-foot shadow on theground assuming that the angle ofelevation from the point on theground at the tip of the shadow tothe sun is 61º. Round your answer tothe nearest foot.2014.19 joan kessler distancemath.com

Answer 1

Let's start by drawing the representation of the given problem. The length of the shadow of the pine tree is given and the angle of elevation. This is drawn as

Given the adjacent side and the angle, we can determine the opposite side of the triangle using the trigonometric function tangent wherein

$\tan \theta=\frac{opposite}{adjacent}$

We are solving for the opposite side, hence, the derived equation to solve the adjacent side based on the equation above will be

$\text{opposite}=(\tan \theta)\times adjacent$

Substitute the values on the equation above and compute

$\text{opposite}=(\tan 61)\times(41ft)=74ft$

Therefore, the height of the pine tree is 74 ft.