A right triangle is shown with an angle that measures 60 degrees. The leg adjacent to the 60 degree angle is labeled 5. The leg opposite of the 60 degree angle is labeled x. The hypotenuse is labeled y.

Question

Find the value of x. If your answer is not an integer, leave it in simplest radical form. The diagram is not drawn to scale.

Answer 1

Using trigonometric ratios, we can solve for x:

sin(60°) = opposite/hypotenuse

sin(60°) = x/y

y = x/sin(60°)

cos(60°) = adjacent/hypotenuse

cos(60°) = 5/y

y = 5/cos(60°)

Since y is equal to y in both equations, we can set them equal to each other:

x/sin(60°) = 5/cos(60°)

x = 5(sin(60°)/cos(60°))

x = 5(tan(60°))

x = 5(sqrt(3))

Therefore, x equals 5√3.