The area of given triangle is 128.1 square inches.
What is area of SAS triangle?
The area of a SAS triangle is the total amount of space it encloses in a 2-dimensional plane. "SAS" which means "Side, Angle, Side", is the property of a triangle whose 2 sides and the angle between these sides is given.
The formula to calculate the area of a triangle using SAS is given as,
1. When sides 'b' and 'c' and included angle A is known, the area of the triangle is: 1/2 × bc × sin(A)
2. When sides 'b' and 'a' and included angle B is known, the area of the triangle is: 1/2 × ab × sin(C)
3. When sides 'a' and 'c' and included angle C is known, the area of the triangle is: 1/2 × ac × sin(B)
Given
a = 24 inches
b = 11 inches
∠C=76°.
Area of SAS triangle = [tex]\frac{1}{2} absinc[/tex]
Area = [tex]\frac{1}{2}(24)(11)sin76^{0}[/tex]
Area = 128.079 ≅ 128.1 (nearest tenth)
Hence, the area of given triangle is 128.1 square inches.
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