Question

Solve for x. Round to the nearest hundredth.

Answer 1

Given that the length of the hypotenuse is 8 and the angle is 42°

The length of the one leg of the triangle is x.

We need to determine the value of x.

Value of x:

The value of x can be determined using the trigonometric ratio.

Thus, we have;

`sin \ \theta=(opp)/(hyp)`

Substituting the values, we get;

`sin \ 42^(\circ)=(x)/(8)`

Multiplying both sides of the equation by 8, we get;

`sin \ 42^(\circ)*8=x`

Simplifying, we get;

`0.669 * 8=x`

`5.352\approx x`

Therefore, the value of x is 5.35(app.)

Hence, Option A is the correct answer.