Questions: Use the inverse of cosine to find the missing angle. Round your answer to the nearest tenth. θ ≈

Transcript text: Use the inverse of cosine to find the missing angle. Round your answer to the nearest tenth. (1 point) $\theta \approx$ $\square$

Solution

Solution Steps

Step 1: Identify the given values

The problem provides the lengths of the adjacent side (9) and the hypotenuse (12) of a right triangle.

Step 2: Set up the inverse cosine function

To find the angle θ, use the inverse cosine function (cos⁻¹). The cosine of an angle in a right triangle is the ratio of the length of the adjacent side to the hypotenuse: \[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{9}{12} \]

Step 3: Calculate the angle using a calculator

Use a calculator to find the inverse cosine of $\frac{9}{12}$: \[ \theta = \cos^{-1}\left(\frac{9}{12}\right) \approx \cos^{-1}(0.75) \]