Question

Can someone help me with this question

Answer 1

Answer:

$w = 2.6$

$x = 26.2^\circ$

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.

$\sin A = \dfrac{opp}{hyp}$

$\sin 32^\circ = \dfrac{w}{5}$

$w = 5 \sin 32^\circ$

$w = 2.6495$

$w = 2.6$

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.

$\sin A = \dfrac{opp}{hyp}$

$\sin x = \dfrac{w}{6}$

$\sin x = \dfrac{2.6495}{6}$

$\sin x = 0.441599$

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.

$x = \sin^{-1} 0.441599$

$x = 26.2^\circ$