A 30-60-90 degree triangle has a hypotenuse 20 cm in length. What is the exact area of the triangle

The exact area is 86.6 square centimeters

Step-by-step explanation: Please refer to the the attached diagram for details.

The triangle according to the question has been drafted showing angles 30, 60 and 90. We shall calculate x (base of the triangle) and y (height of the triangle) before applying the formula for area of a triangle which is

A= 1/2 x B x H

To calculate x,

Sin 30 = opposite/hypotenuse

Sin 30 = x/20

Sin30 (20) = x

0.5 (20) = x

10 = x

To calculate y,

Sin 60 = opposite/hypotenuse

Sin60 = y/20

Sin60 (20) = y

0.8660 (20) = y

17.32 = y

Having determined x (Base) = 10, and y (Height) = 17.32

The area of the triangle is calculated as

Area = 1/2 x B x H

Area = 1/2 x 10 x 17.32

Area = 5 x 17.32

Area = 86.6 square centimeters