Question

value: 3
solve for the long - leg and for the hypotenuse of the 30 - 60 - 90 triangle.
60°
10
o a. a = 20 and b = 10
o b. a = 20 and b = 10√3
o c. a = 10 and b = 10√3
o d. a = 10√3 and b = 20

Explanation:

Step1: Recall 30 - 60 - 90 triangle ratios

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

Step2: Find the long - leg

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

Step3: Find the hypotenuse

The hypotenuse $a$ is given by the formula $a=2x$. Substituting $x = 10$, we get $a = 20$.

Answer:

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