Question

solve for ( x ). round to the nearest tenth, if necessary.
(image of a right triangle wty with right angle at t, angle at y is 72°, side ty is 3.9, and hypotenuse wy is ( x ))

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( WTY \), \( \angle T = 90^\circ \), \( \angle Y = 72^\circ \), \( TY = 3.9 \), and hypotenuse \( WY = x \). We use the cosine ratio: \( \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}} \). Here, \( \cos(72^\circ)=\frac{TY}{WY}=\frac{3.9}{x} \).

Step2: Solve for \( x \)

Rearrange the formula: \( x = \frac{3.9}{\cos(72^\circ)} \). Calculate \( \cos(72^\circ) \approx 0.3090 \). Then \( x=\frac{3.9}{0.3090}\approx 12.6 \).

Answer:

\( 12.6 \)