Question

In a right triangle, the hypotenuse is 45 inches long . What is the length of the side opposite a 60 degree angle ?

Answer 1

We have a right triangle with hypotenuse 45 in. long.

We have to find the length of the opposite side to a 60° angle.

We can use the trigonometric ratio:

`\sin (\alpha)=\frac{\text{Opposite}}{\text{Hypotenuse}}=(x)/(H)`

Then, as α = 60° and H = 45 in., we can write:

`\begin{gathered} x=H\cdot\sin (\alpha) \\ x=45\cdot\sin (60\degree) \\ x=45\frac{\sqrt[]{3}}{2} \\ x\approx38.97 \end{gathered}`

Answer: the opposite side will have a length of approximate 38.97 inches.