Question

question 16 of 25
in the triangle below, what is the length of the side opposite the 60° angle?
a. 3√3
b. √3
c. 3
d. 6

Explanation:

Step1: Recall 30 - 60 - 90 triangle ratio

In a 30 - 60 - 90 triangle, if the hypotenuse $c$ is given and the sides are in the ratio $1:\sqrt{3}:2$ (shorter leg : longer leg : hypotenuse). Let the hypotenuse $c = 2\sqrt{3}$.

Step2: Find the side opposite 60°

The side opposite the 60° angle is the longer leg. If the hypotenuse $c = 2\sqrt{3}$ and the ratio of the hypotenuse to the longer - leg is $2:\sqrt{3}$. Let the side opposite 60° be $x$. We know that $\frac{c}{x}=\frac{2}{\sqrt{3}}$. Substituting $c = 2\sqrt{3}$ into $\frac{2\sqrt{3}}{x}=\frac{2}{\sqrt{3}}$. Cross - multiply gives $2x=2\sqrt{3}\times\sqrt{3}$, so $2x = 6$ and $x = 3$.

Answer:

C. 3