Questions: Find the angle measure of θ.

Transcript text: Find the angle measure of $\theta$.

Solution

Solution Steps

Step 1: Identify the sides of the right triangle

In the given right triangle, we have:

Opposite side to angle $\theta$ : $12$ (side $BC$ )
Adjacent side to angle $\theta$ : $7$ (side $AB$ )

Step 2: Use the tangent function

The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. Therefore, we can write: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{12}{7}$

Step 3: Calculate the angle using the arctangent function

To find the angle $\theta$ , we take the arctangent (inverse tangent) of $\frac{12}{7}$ : $\theta = \tan^{-1}\left(\frac{12}{7}\right)$

Using a calculator: $\theta \approx \tan^{-1}(1.714) \approx 59.74^\circ$

Final Answer

$\theta \approx 59.74^\circ$

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