Question

solve for x. round to the nearest tenth, if necessary.
(image of a right triangle nop with right angle at o, side on = 73, angle at n is 32 degrees, and hypotenuse np = x)
answer attempt 2 out of 2
x = |

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \( ONP \), we know the adjacent side to angle \( N \) (which is \( 32^\circ \)) is \( ON = 73 \), and the hypotenuse is \( x \) ( \( NP=x \) ). The cosine of an angle in a right triangle is defined as the adjacent side divided by the hypotenuse. So we use the cosine function: \( \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}} \)
So, \( \cos(32^\circ)=\frac{73}{x} \)

Step2: Solve for \( x \)

We can rearrange the formula to solve for \( x \). Multiply both sides by \( x \): \( x\cos(32^\circ)=73 \)
Then divide both sides by \( \cos(32^\circ) \): \( x = \frac{73}{\cos(32^\circ)} \)
Now, we calculate \( \cos(32^\circ) \approx 0.8480 \) (using a calculator)
So, \( x=\frac{73}{0.8480}\approx 86.1 \)

Answer:

\( 86.1 \)