Question

the hypotenuse of a 30° - 60° - 90° triangle has a length of 12 cm. which could be the length of a leg of the triangle? select all that apply.
a. 8 cm
b. 10 cm
c. 6 cm
d. 6√3 cm

Explanation:

Step1: Recall the properties of a 30 - 60 - 90 triangle

In a 30 - 60 - 90 triangle, if the hypotenuse \(c = 12\) cm, the side opposite the 30° angle \(a=\frac{c}{2}\), and the side opposite the 60° angle \(b = \frac{c\sqrt{3}}{2}\).

Step2: Calculate the lengths of the legs

• For the side opposite the 30° angle: \(a=\frac{12}{2}=6\) cm.
• For the side opposite the 60° angle: \(b=\frac{12\sqrt{3}}{2}=6\sqrt{3}\) cm.

Answer:

C. \(6\) cm, D. \(6\sqrt{3}\) cm