Question

Use the inverse of tangent to solve for the approximate angle measure of vertex C, rounded to the nearest whole degree. Hypotenuse is 15, adjacent is 12, and the opposite is 9.

53 degrees
37 degrees
39 degrees
59 degrees

Answers

GPT-4o mini
To find the angle measure of vertex \( C \) using the inverse tangent function, we'll first identify the relevant sides of the triangle:

- The side opposite angle \( C \) is 9.
- The side adjacent to angle \( C \) is 12.

We can use the tangent function, which is defined as:

\[
\tan(C) = \frac{\text{opposite}}{\text{adjacent}} = \frac{9}{12}
\]

Now, we will calculate \( C \) using the inverse tangent function:

\[
C = \tan^{-1}\left(\frac{9}{12}\right)
\]

Calculating \( \frac{9}{12} \):

\[
\frac{9}{12} = 0.75
\]

Now we will use the inverse tangent:

\[
C = \tan^{-1}(0.75)
\]

Using a calculator to find \( \tan^{-1}(0.75) \):

\[
C \approx 36.87 \text{ degrees}
\]

Rounding to the nearest whole degree:

\[
C \approx 37 \text{ degrees}
\]

Thus, the approximate measure of angle \( C \) is \( \boxed{37} \) degrees.

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