Problem

Find the angle $\theta$, in radians, in the given right triangle. The length of the side adjacent to $\theta$ is 16 and the length of the side opposite $\theta$ is 13 .

Answer

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Answer

\(\boxed{\theta \approx 0.682 \text{ radians}}\)

Steps

Step 1 ：Given a right triangle with side lengths adjacent to $\theta$ as 16 and opposite to $\theta$ as 13.

Step 2 ：Use the tangent function to find the angle $\theta$: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{13}{16}$

Step 3 ：Find the angle $\theta$ using the inverse tangent function: $\theta = \arctan\left(\frac{13}{16}\right)$

Step 4 ：Calculate the angle $\theta$ in radians: $\theta \approx 0.682$ radians

Step 5 ：\(\boxed{\theta \approx 0.682 \text{ radians}}\)

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