Question

Solve the right triangle for x.

Answer 1

Given:

The given figure is a right triangle.

The measure of one of the angle is 37°

One of the length of the legs of the triangle is 11 cm

The length of the hypotenuse 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;

$cos \ \theta=\frac{adj}{hyp}$

Substituting the values, we have;

$cos \ 37^{\circ}=\frac{11}{x}$

Simplifying, we get;

$x=\frac{11}{cos \ 37^{\circ}}$

$x=\frac{11}{0.799}$

$x=13.767$

Rounding off to the nearest hundredth, we get;

$x=13.77$

Thus, the value of x is 13.77 cm.