Question

solve for the short leg of the 30 - 60 - 90 triangle.
4
60°
b
o a. b = 2
o b. b = 4
o c. b = 4√3
o d. b = 2√3

Explanation:

Step1: Recall 30 - 60 - 90 triangle ratio

In a 30 - 60 - 90 triangle, if the hypotenuse is $c$, the short - leg (opposite the 30° angle) is $a$, and the long - leg (opposite the 60° angle) is $b$, the ratio of the sides is $a:b:c = 1:\sqrt{3}:2$.

Step2: Identify given values

Here, the hypotenuse $c = 4$.

Step3: Calculate the short - leg

Let the short - leg be $x$. Since $c = 2x$ (from the ratio), and $c = 4$, then $2x=4$, so $x = 2$.

Answer:

A. $b = 2$