Look at the right triangle below.

Question

A right triangle with interior angles that measure 67 degrees and 23 degrees. The side opposite the 23-degree angle is labeled x, and the hypotenuse is labeled 17 centimeters.

Which trigonometric ratio can be used to find the length of the side of the triangle labeled x?

A.
tan 67°

B.
cos 23°

C.
sin 67°

D.
sin 23°

Answer 1

To find the length of the side opposite the 23-degree angle (labeled \(x\)) in a right triangle where the hypotenuse is known (17 cm), you can use the sine function.

The sine function relates the angle to the ratio of the length of the opposite side to the length of the hypotenuse. Specifically, the sine of an angle in a right triangle is defined as follows:

\[ \sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}} \]

For the 23-degree angle:

\[ \sin(23°) = \frac{x}{17} \]

So, the correct trigonometric ratio to use to find \(x\) is:

D. sin 23°