Answer:
[tex] w = 2.6 [/tex]
[tex] x = 26.2^\circ [/tex]
Step-by-step explanation:
Solving for w:
Look at the right triangle on the left side. It has a 32-deg angle, a hypotenuse of length 5, and a leg of length w. For the 32-deg angle, w is the opposite leg. We have an opposite leg and a hypotenuse, so we use the sine.
[tex] \sin A = \dfrac{opp}{hyp} [/tex]
[tex] \sin 32^\circ = \dfrac{w}{5} [/tex]
[tex] w = 5 \sin 32^\circ [/tex]
[tex] w = 2.6495 [/tex]
[tex] w = 2.6 [/tex]
Solving for x:
Now look at the right triangle on the right side. There is an acute angle measuring x, an opposite leg measuring 2.6495 (from the solution above), and a hypotenuse measuring 6. We use the sine again.
[tex] \sin A = \dfrac{opp}{hyp} [/tex]
[tex] \sin x = \dfrac{w}{6} [/tex]
[tex] \sin x = \dfrac{2.6495}{6} [/tex]
[tex] \sin x = 0.441599 [/tex]
Since we know what the sine of angle x is equal to, and we want to know the measure of angle x, we use the inverse sine function, also called the arcsine.
[tex] x = \sin^{-1} 0.441599 [/tex]
[tex] x = 26.2^\circ [/tex]
