A triangle has angles that measure 30,60, and 90. The hypotnuse of the triangle measures 10 inches. Which is the best estimate f

Question

3 years ago

13

or the perimeter of the triangle? Round to the nearest tenth

2 answers:

ElenaW [278] · Answer 1 · 2022-05-15T20:18:05+03:00

6 0

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

Marta_Voda [28] · Answer 2 · 2022-05-15T22:37:22+03:00

Answer:

The required perimeter is 23.7 inches.

Step-by-step 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.