Question

solve for the long leg and for the hypotenuse of the 30 - 60 - 90 triangle.

60°
10

a. a = 20 and b = 10
b. a = 20 and b = 10\sqrt{3}
c. a = 10 and b = 10\sqrt{3}
d. a = 10\sqrt{3} and b = 20

Explanation:

Step1: Recall 30 - 60 - 90 triangle ratios

In a 30 - 60 - 90 triangle, if the shorter leg (opposite the 30° angle) is $x$, the longer leg (opposite the 60° angle) is $x\sqrt{3}$ and the hypotenuse is $2x$. Here the shorter leg is 10.

Step2: Calculate the long - leg

The long - leg $b$ (opposite the 60° angle) is given by the formula $b = 10\sqrt{3}$ since the shorter leg is 10.

Step3: Calculate the hypotenuse

The hypotenuse $a$ is given by the formula $a=2\times10 = 20$ since the shorter leg is 10.

Answer:

B. $a = 20$ and $b = 10\sqrt{3}$