Question

find α in degrees.
round to the nearest hundredth.

Explanation:

Step1: Recall the tangent function

In a right - triangle, \(\tan\alpha=\frac{\text{opposite}}{\text{adjacent}}\). Here, the opposite side to \(\alpha\) is \(\sqrt{15}\) and the adjacent side is \(7\). So, \(\tan\alpha=\frac{\sqrt{15}}{7}\).

Step2: Calculate \(\alpha\)

We know that \(\alpha = \tan^{- 1}(\frac{\sqrt{15}}{7})\). First, calculate \(\frac{\sqrt{15}}{7}\approx\frac{3.87298}{7}\approx0.5533\). Then, \(\alpha=\tan^{-1}(0.5533)\). Using a calculator, \(\alpha\approx29.05^{\circ}\).

Answer:

\(29.05\)