Question

Find the indiciated angle and round the answer to the nearest hundredth Question b

Answer 1

Given two sides of a right triangle, to find a missing angle, follow the steps below.

Step 01: Find an adequate trigonometric identity.

Since the two legs of the triangle are known, use the equation for a tangent:

`\text{tan(}\theta)=\frac{\text{opposite}}{\text{adjacent}}`

Step 02: Substitute the values in the equation.

In this exercise,

8 is the opposite side;

5 is the adjacent side to θ.

Then,

`\begin{gathered} \tan (\theta)=(8)/(5) \\ \tan (\theta)=1.6 \end{gathered}`

Step 03: Find θ.

Use tan⁻¹ to find θ.

`\begin{gathered} \theta=\tan ^(-1)(1.6) \\ \theta=57.99\degree \end{gathered}`

Answer: θ = 57.99°.