Answer:the area of triangle ABC is
346.4 feet^2
Step-by-step explanation:
The given triangle ABC is shown in the attached photo.
The formula for determining the area of a triangle is expressed as
Area = 1/2(abSinC) = 1/2(bcSinA)
A = 60 degrees
b = 40 feet
c = 20 feet
Therefore, area of the triangle is
1/2(bcSinA) = 1/2(40 × 20 × Sin60)
= 1/2 × 40 × 20 × 0.8660
= 346.4 feet^2
Alternatively, we can apply Heron's formula. We would determine the length of a by applying cosine rule,
a^2 = b^2 + c^2 -2bcCosA
Then, Heron's formula is expressed as
Area = √S(S - a)(S- b)(S - c)
Where S = (a + b + c)/2
