Question

the angle of elevation to a nearby tree from a point on the ground is measured to be 31°. how tall is the tree if the point on the ground is 88 feet from the bottom of the tree? round your answer to the nearest tenth of a foot if necessary. 88 x answer attempt 1 out of 2

Explanation:

Step1: Identify the trigonometric relationship

We have a right triangle where the adjacent side to the \(31^\circ\) angle is 88 feet (distance from the point to the bottom of the tree), and the opposite side is \(x\) (height of the tree). We use the tangent function, which is \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\). So \(\tan(31^\circ)=\frac{x}{88}\).

Step2: Solve for \(x\)

Multiply both sides by 88: \(x = 88\times\tan(31^\circ)\). Calculate \(\tan(31^\circ)\approx0.6009\). Then \(x = 88\times0.6009\approx52.9\).

Answer:

\(52.9\) feet