Questions: Find the angle measure of θ.

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

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Solution Steps

Step 1: Identify the sides of the right triangle

In the given right triangle, we have:

  • Opposite side to angle θ \theta : 12 12 (side BC BC )
  • Adjacent side to angle θ \theta : 7 7 (side AB 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(θ)=oppositeadjacent=127 \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{12}{7}

Step 3: Calculate the angle using the arctangent function

To find the angle θ \theta , we take the arctangent (inverse tangent) of 127 \frac{12}{7} : θ=tan1(127) \theta = \tan^{-1}\left(\frac{12}{7}\right)

Using a calculator: θtan1(1.714)59.74 \theta \approx \tan^{-1}(1.714) \approx 59.74^\circ

Final Answer

θ59.74 \theta \approx 59.74^\circ

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