Question

The length of the hypotenuse of a 30°-60°-9° triangle is 8. find the perimeter

Answer 1

The perimeter is all side plus together

hypotenuse(2x)= 8

then x=4

the side that is perpendicular is (x√3)=4√3=6.92

the other side(x)= 4

The perimeter is 8+4+6.92=18.92

Answer 2

The perimeter is

12 + 4root3

A decimal approximation for this value is 18.93

Explanation:

30° -60°-90° triangles are very special. There are fabulous SHORTCUTS for calculating the lengths of the sides of the triangle.

The hypotenuse is the longest side, it is DOUBLE the shortest side (short leg). The short leg is HALF the hypotenuse.

Your triangle has hypotenuse 8, so the short leg is 4.

Another SHORTCUT: The long leg is the short leg × root3. So your triangle has a short leg 4, so the long leg is 4root3.

Perimeter means the distance all the way around the shape. So add all three sides.

8 + 4 + 4root3

12 + 4root3

approx= 18.93