Question

What is the angle measurement of x?

Imagine a right triangle. The left side of the triangle is labelled 5.0, the slanted side on the right is labelled 9.2, and the bottom side is labelled 7.7
In the bottom right corner is an x with a degree sign next to it.

A. x = 90.3 degrees
B. x = 57.1 degrees
C. x = 56 degrees
D. x = 32.9 degrees

Answer 1

To find the angle \( x \) in the right triangle with sides 5.0 (adjacent), 7.7 (opposite), and 9.2 (hypotenuse), we can use trigonometric functions.

We will use the sine, cosine, or tangent functions as appropriate. Since we know the lengths of all the sides, we can use the tangent function, which is defined as:

\[
\tan(x) = \frac{\text{opposite}}{\text{adjacent}}
\]

Here, the opposite side is 7.7 and the adjacent side is 5.0. Thus:

\[
\tan(x) = \frac{7.7}{5.0}
\]

Calculating that gives:

\[
\tan(x) = 1.54
\]

We can now find the angle \( x \) using the arctangent function:

\[
x = \tan^{-1}(1.54)
\]

Using a calculator to find the arctangent gives:

\[
x \approx 57.1 \text{ degrees}
\]

Thus, the correct answer is:

**B. x = 57.1 degrees**.