Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A right triangle is shown with an angle that measures 24 degrees. The leg adjacent to the 24 degree angle is 11. The hypotenuse is x.
Find the value of x. Round to the nearest tenth. The diagram is not drawn to scale.
(2 points)
To find the value of x, we can use the trigonometric ratio of cosine since we have the adjacent leg and the hypotenuse.
cos(24°) = adjacent / hypotenuse
cos(24°) = 11 / x
To find x, we first need to find the cosine of 24 degrees. We can do this using a calculator.
cos(24°) ≈ 0.9135
Now we can plug in this value into the equation:
0.9135 = 11 / x
Solving for x:
x = 11 / 0.9135
x ≈ 12
Therefore, the value of x, the hypotenuse, is approximately 12 units.