Question

question
the angle of elevation to a nearby tree from a point on the ground is measured to be 55°. how tall is the tree if the point on the ground is 90 feet from the bottom of the tree? round your answer to the nearest hundredth of a foot if necessary.

Explanation:

Step1: Recall the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 55^{\circ}\), the adjacent side \(a = 90\) feet, and the opposite side (height of the tree) is \(x\). So, \(\tan(55^{\circ})=\frac{x}{90}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\tan(55^{\circ})=\frac{x}{90}\) by \(90\). We get \(x = 90\times\tan(55^{\circ})\).
Since \(\tan(55^{\circ})\approx1.428148\), then \(x=90\times1.428148\).
\(x = 128.53332\)

Answer:

\(128.53\) feet