This lesson will show you how to find the area of a triangle given sas. Suppose you are trying to find the area of the triangle below.
In order to use the formula above, we need to know what the height is. Thus, let us write an expression that will have the height in it. The sine ratio will help you achieve this.
Solve for h by multiplying both sides by c.
h = c(sin A)
Substitute c(sin A) for h in the formula for the area shown above.
A backyard is shaped like a triangle. The lengths of two adjacent sides of the triangular backyard are 50 feet and 65 feet. The angle between the sides is 30 degrees. Find the area of the backyard.
Let b = 50 feet, c = 65 feet, A = 30 degrees, and sin (30 degrees) = 0.5
Area = 25 × 65 × 0.5
Area = 25 × 32.5
Area = 812.5 ft2