Question

1. you are floating in an inner - tube on lake michigan, 260 feet away from the iconic little sable point lighthouse. you remember reading in the brochure that the lighthouse is 107 feet tall. at what angle do you have to look up to see the top of the lighthouse?

Explanation:

Step1: Identify the trigonometric ratio

We have a right - triangle situation where the adjacent side \(x = 260\) feet and the opposite side \(y=107\) feet. We use the tangent ratio \(tan\theta=\frac{opposite}{adjacent}\). So, \(tan\theta=\frac{107}{260}\).

Step2: Solve for \(\theta\)

Take the inverse tangent (arctan) of both sides. \(\theta=\arctan(\frac{107}{260})\).
Using a calculator, \(\frac{107}{260}\approx0.4115\). Then \(\theta=\arctan(0.4115)\approx22.4^{\circ}\)

Answer:

The angle is approximately \(22.4^{\circ}\)