Question

Triangle XYZ is a right triangle with the right angle being located at X the opposite leg is labeled a the hypotenuse is labeled c the adjacent leg is labeled b.

Which trigonometric equation do you need to find side c if m<Y = 52 degrees and b=9.2.

A. tan (52) = c/9.2
B. cos (52) = 9.2/c
C. sin (52) = 9.2/c
D. cos (52) = b/ 9.2

Answer 1

To find the length of the hypotenuse \( c \) in a right triangle, we can use the cosine function, which relates the adjacent side and the hypotenuse.

In triangle XYZ:
- \( m<Y = 52^\circ \)
- \( b = 9.2 \) (the length of the adjacent side)

The cosine function is defined as:

\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]

In this case, it can be written as:

\[
\cos(52) = \frac{b}{c}
\]

Rearranging this, we want:

\[
c = \frac{b}{\cos(52)}
\]

Since we know \( b = 9.2 \), we can substitute to get the relationship:

\[
\cos(52) = \frac{9.2}{c}
\]

This leads us to the choice that equals that arrangement:

**B.** \( \cos(52) = \frac{9.2}{c} \)

This means the correct answer to find side \( c \) is indeed option **B**.