Question

A triangle has angles that measure 30,60, and 90. The hypotnuse of the triangle measures 10 inches. Which is the best estimate for the perimeter of the triangle? Round to the nearest tenth

Answer 1

The best estimate for the perimeter of this triangle would about 23.7 inches. Hope this helps!

Answer 2

The required perimeter is 23.7 inches.

Explanation:

Consider the provided measure 30,60, and 90

The ratio of side in 30-60-90 is:

Side opposite to the 30° angle is x

Side opposite to the 60° angle is x × √3

Side opposite to the 90° angle is 2x

The hypotenuse of the triangle measures 10 inches.

Side opposite to the 90° is known as the hypotenuse.

Thus,

`2x=10`

`x=5`

The side opposite to the 30° angle is 5 inches.

The side opposite to the 60° angle is x × √3 = 5×√3 = 8.7 inches (nearest tenth)

The perimeter is the sum of all sides:

5+10+8.7=23.7 inches

Hence, the required perimeter is 23.7 inches.