Question

solve the right triangle.
write your answers in simplified, rationalized form. do not round.
$wx =$
$vx =$
$m\angle w =$

Explanation:

Step1: Find \(m\angle W\)

In a right - triangle, the sum of the two non - right angles is \(90^{\circ}\).
Since \(\angle V = 60^{\circ}\) and \(\angle X=90^{\circ}\), then \(m\angle W=90^{\circ}-m\angle V\).
\(m\angle W = 90^{\circ}-60^{\circ}=30^{\circ}\).

Step2: Find \(VX\)

We know that \(\cos V=\frac{VX}{WV}\). Given \(WV = 10\) and \(V = 60^{\circ}\), and \(\cos60^{\circ}=\frac{1}{2}\).
So \(VX=WV\times\cos V\).
\(VX = 10\times\cos60^{\circ}=10\times\frac{1}{2}=5\).

Step3: Find \(WX\)

We know that \(\sin V=\frac{WX}{WV}\). Given \(WV = 10\) and \(V = 60^{\circ}\), and \(\sin60^{\circ}=\frac{\sqrt{3}}{2}\).
So \(WX=WV\times\sin V\).
\(WX = 10\times\sin60^{\circ}=10\times\frac{\sqrt{3}}{2}=5\sqrt{3}\).

Answer:

\(WX = 5\sqrt{3}\)
\(VX = 5\)
\(m\angle W=30^{\circ}\)