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Question

The sides and angles of a triangle are labeled. The adjacent side is labeled 9, the hypotenuse is labeled 12, and the angle where the adjacent side and the hypotenuse meet is labeled with the theta symbol. The right angle is marked with a small box.

Use the inverse of cosine to find the missing angle. Round your answer to the nearest tenth.

(1 point)
θ≈
°

Answer 1

To find the angle θ in a right triangle where you have the adjacent side (9) and the hypotenuse (12), you can use the cosine function:

\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{9}{12} \]

First, simplify the fraction:

\[ \frac{9}{12} = 0.75 \]

Now, to find θ, use the inverse cosine (arccos):

\[ \theta = \cos^{-1}(0.75) \]

Using a calculator:

\[ \theta \approx 41.4^\circ \]

So, rounding to the nearest tenth:

\[ \theta \approx 41.4^\circ \]

Thus, the final answer is:

\(\theta \approx 41.4°\)