Answer: 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
