Question

find vw.
write your answer as an integer or as a decimal rounded to the nearest tenth.
vw =

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \( UVW \) with right angle at \( V \), we know the hypotenuse \( UW = 9.1 \) and angle \( \angle U = 33^\circ \). We need to find the length of \( VW \), which is the side opposite to angle \( U \). The sine function relates the opposite side and the hypotenuse: \( \sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}} \). So, \( \sin(33^\circ)=\frac{VW}{UW} \).

Step2: Solve for \( VW \)

Substitute \( UW = 9.1 \) and \( \theta = 33^\circ \) into the formula: \( VW = UW\times\sin(33^\circ) \). Calculate \( \sin(33^\circ) \approx 0.5446 \). Then \( VW = 9.1\times0.5446 \approx 4.95586 \). Rounding to the nearest tenth gives \( VW \approx 5.0 \).

Answer:

\( 5.0 \)