Question

Triangle ABC is a sketch of a triangular flower bed that has an area of 65.1 square feet.

Trigonometric area formula: Area =

Answer 1

40 ft

Explanation:

Triangle ABC is given by AB = 13 ft, BC = 10 ft, ∠ACB = 50° and AC = b. Let AB = a = 13 ft, BC = c = 10 ft

Since two sides are given and one angle is given, to find the other side, we use the cosine formula. The cosine formula is given by:

`c^2=a^2+b^2-2abcos(C)\\b^2=c^2-a^2+2abcos(C)\\substituting\ values:\\b^2=13^2-10^2+2*10*bcos(50)\\b^2=169-100+12.86b\\b^2-12.86b=69\\b^2-12.86b-69=0\\ solving\ simultaneously\ gives:\\b=16.93\ ft`

The perimeter of the triangle is given by:

Perimeter = AB + BC + AC = 13 + 10 +16.93 = 39.93 ft ≈ 40 ft