Question

Can someone help me with this question

Answer 1

`w = 2.6`

`x = 26.2^\circ`

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 = (opp)/(hyp)`

`\sin 32^\circ = (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 = (opp)/(hyp)`

`\sin x = (w)/(6)`

`\sin x = (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`