<u>Given</u>:
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.
<u>Value of x:</u>
The value of x can be determined using the trigonometric ratio.
Thus, we have;
![cos \ \theta=\frac{adj}{hyp}](https://tex.z-dn.net/?f=cos%20%5C%20%5Ctheta%3D%5Cfrac%7Badj%7D%7Bhyp%7D)
Substituting the values, we have;
![cos \ 37^{\circ}=\frac{11}{x}](https://tex.z-dn.net/?f=cos%20%5C%2037%5E%7B%5Ccirc%7D%3D%5Cfrac%7B11%7D%7Bx%7D)
Simplifying, we get;
![x=\frac{11}{cos \ 37^{\circ}}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B11%7D%7Bcos%20%5C%2037%5E%7B%5Ccirc%7D%7D)
![x=\frac{11}{0.799}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B11%7D%7B0.799%7D)
![x=13.767](https://tex.z-dn.net/?f=x%3D13.767)
Rounding off to the nearest hundredth, we get;
![x=13.77](https://tex.z-dn.net/?f=x%3D13.77)
Thus, the value of x is 13.77 cm.