Question

solve the right triangle.

write your answers as integers or as decimals rounded to the nearest tenth.
vw =
wx =
m∠w = °

Explanation:

Step1: Find \( m\angle W \)

In a right triangle, the sum of the acute angles is \( 90^\circ \). Given \( \angle V = 59^\circ \) and \( \angle X = 90^\circ \), we have \( m\angle W=90^\circ - 59^\circ = 31^\circ \).

Step2: Find \( VW \) (hypotenuse)

We know that \( \cos(59^\circ)=\frac{VX}{VW} \), where \( VX = 4 \). So \( VW=\frac{VX}{\cos(59^\circ)} \).
Since \( \cos(59^\circ)\approx0.5150 \), then \( VW=\frac{4}{0.5150}\approx7.8 \).

Step3: Find \( WX \) (opposite side to \( \angle V \))

We use \( \tan(59^\circ)=\frac{WX}{VX} \), so \( WX = VX\times\tan(59^\circ) \).
Since \( \tan(59^\circ)\approx1.6643 \), then \( WX = 4\times1.6643\approx6.7 \).

Answer:

\( VW \approx 7.8 \)
\( WX \approx 6.7 \)
\( m\angle W = 31^\circ \)