Question

"22.

What is the area of a 30°-60°-90°
triangle with hypotenuse length of 16?
F 16
G 32
H 32V3
J 6413"What is the area of a 30°-60°-90° triangle with a hypotenuse length of 16?

A) 16
B) 32
C) \(32\sqrt{3}\)
D) \(64\sqrt{3}\)

Answer 1

The area of a triangle with hypotenuse length of 16 in a 30°-60°-90° triangle can be found using the formula A = 1/2 × base × height. The area is 32√3.

Step-by-step explanation:

In a 30°-60°-90° triangle, the ratio of the side lengths is 1:√3:2. Since the hypotenuse length is 16, we can find the lengths of the other two sides.

The side opposite the 30° angle is 16/2 = 8, and the side opposite the 60° angle is 8√3.

To find the area of the triangle, we can use the formula A = 1/2 × base × height. The base of the triangle is 8, and the height is 8√3. Plugging these values into the formula, we get:

A = 1/2 × 8 × 8√3 = 32√3

Therefore, the area of the triangle is 32√3.