Question

1. determine the angle of inclination of the line to the nearest tenth of a degree. (diagram: right triangle with vertical side labeled 4.2, horizontal dashed side labeled 6.7)

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle where the opposite side to the angle of inclination (\(\theta\)) is \(4.2\) and the adjacent side is \(6.7\). So we use the tangent function: \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}=\frac{4.2}{6.7}\)

Step2: Calculate the angle

First, find \(\frac{4.2}{6.7}\approx0.6269\). Then, take the arctangent (inverse tangent) of \(0.6269\): \(\theta=\arctan(0.6269)\)
Using a calculator, \(\theta\approx32.1^\circ\) (rounded to the nearest tenth of a degree)

Answer:

\(32.1^\circ\)