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;

$sin \ \theta=\frac{opp}{hyp}$

Substituting the values, we get;

$sin \ 42^{\circ}=\frac{x}{8}$

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

$sin \ 42^{\circ}\times8=x$

Simplifying, we get;

$0.669 \times 8=x$

      $5.352\approx x$

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

Hence, Option A is the correct answer.