Question

1. a dog is standing 5 feet from the base of a tree, looking up at a cat that has climbed 16 feet up the tree. what is the angle of elevation from the point the dog is standing on the ground to the cat?

Explanation:

Step1: Identify the sides of the right - triangle

We have a right - triangle where the adjacent side \(x = 5\) (distance from the dog to the base of the tree) and the opposite side \(y=16\) (height of the cat up the tree).

Step2: Use the tangent function

The tangent of an angle of elevation \(\theta\) in a right - triangle is given by \(\tan\theta=\frac{y}{x}\). Substituting \(x = 5\) and \(y = 16\), we get \(\tan\theta=\frac{16}{5}=3.2\)

Step3: Find the angle \(\theta\)

To find \(\theta\), we take the inverse tangent (arctan) of \(3.2\). So, \(\theta=\arctan(3.2)\)
Using a calculator, \(\theta\approx72.65^{\circ}\)

Answer:

The angle of elevation is approximately \(72.65^{\circ}\)