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=(adj)/(hyp)`

Substituting the values, we have;

`cos \ 37^(\circ)=(11)/(x)`

Simplifying, we get;

`x=(11)/(cos \ 37^(\circ))`

`x=(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.