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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