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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.
To find the value of x, we can use the cosine function since we have the adjacent leg and the hypotenuse.
Cos(24 degrees) = adjacent / hypotenuse
Cos(24 degrees) = 11 / x
Using a scientific calculator, we can find the cosine of 24 degrees to be approximately 0.9135:
0.9135 = 11 / x
To solve for x, we can rearrange the equation:
x = 11 / 0.9135
x ≈ 12
Therefore, the value of x (the hypotenuse) is approximately 12 when rounded to the nearest tenth.