Question

solve for x. round to the nearest tenth, if necessary.
image of right triangle ytz with right angle at y, side tz = 40, angle at z is 20 degrees, side yz = x
answer attempt 1 out of 2
x = input box submit answer

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( YTZ \), \( \angle Y = 90^\circ \), hypotenuse \( TZ = 40 \), adjacent side to \( \angle Z = 20^\circ \) is \( YZ = x \). We use cosine: \( \cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}} \).
\( \cos(20^\circ)=\frac{x}{40} \)

Step2: Solve for \( x \)

Multiply both sides by 40: \( x = 40\times\cos(20^\circ) \)
Calculate \( \cos(20^\circ)\approx0.9397 \), so \( x\approx40\times0.9397 = 37.588 \)

Step3: Round to nearest tenth

\( 37.588\approx37.6 \)

Answer:

\( x \approx 37.6 \)