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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 side and the hypotenuse:
cos(24°) = adjacent / hypotenuse
cos(24°) = 11 / x
To solve for x, first find the cosine of 24 degrees:
cos(24°) ≈ 0.9063
Now, plug in the known values:
0.9063 = 11 / x
To isolate x, multiply both sides by x:
0.9063x = 11
Then, divide both sides by 0.9063 to solve for x:
x ≈ 11 / 0.9063
x ≈ 12.1392
Therefore, the value of x (rounded to the nearest tenth) is approximately 12.1.