Questions: The diagram below shows a right triangle that has side lengths of 7.37 and 3.12 cm. One of the interior angles of the triangle measures θ degrees. Note that this question allows you to use trig functions that evaluate for angle measures in degrees. What is the value of θ? θ =

The diagram below shows a right triangle that has side lengths of 7.37 and 3.12 cm. One of the interior angles of the triangle measures θ degrees. Note that this question allows you to use trig functions that evaluate for angle measures in degrees. What is the value of θ? θ =
Transcript text: The diagram below shows a right triangle that has side lengths of 7.37 and 3.12 cm . One of the interior angles of the triangle measures $\theta$ degrees. Note that this question allows you to use trig functions that evaluate for angle measures in degrees. To remind yourself how to evaluate trig functions for angle measures in degrees in this program, click here. What is the value of $\theta$ ? $\theta=$ $\square$ Preview
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Solution

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Solution Steps

Step 1: Identify the given values

We are given a right triangle with the side adjacent to angle θ measuring 7.37 cm and the side opposite to angle θ measuring 3.12 cm.

Step 2: Choose the appropriate trigonometric function

Since we have the opposite and adjacent sides relative to angle θ, we use the tangent function: tan(θ) = opposite/adjacent

Step 3: Substitute the given values

tan(θ) = 3.12 cm / 7.37 cm tan(θ) ≈ 0.4233

Step 4: Calculate the angle

θ = arctan(0.4233) θ ≈ 22.93°

Final Answer

θ ≈ 22.93°

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