Question

angle of elevation examples: adrian lara

1. a hiker is standing 220 feet from the base of a hill. the angle of elevation from where he is standing to the top of the hill is ( 29^{circ} ). how tall is the hill?

Explanation:

Step1: Identify the trigonometric ratio

We have a right - triangle where the adjacent side to the angle of elevation (\(\theta = 29^{\circ}\)) is \(x = 220\) feet and we need to find the opposite side \(y\) (height of the hill). The tangent ratio is \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). So, \(\tan\theta=\frac{y}{x}\).

Step2: Substitute the values

Substitute \(\theta = 29^{\circ}\) and \(x = 220\) into the formula \(\tan\theta=\frac{y}{x}\). We get \(y=x\tan\theta\). Since \(\tan(29^{\circ})\approx0.5543\) and \(x = 220\), then \(y = 220\times\tan(29^{\circ})\).

Step3: Calculate the value

\(y=220\times0.5543=121.946\approx122\) feet.

Answer:

The height of the hill is approximately \(122\) feet.