Triangle ABC is a sketch of a triangular flower bed that has an area of 65.1 square feet. Triangle A B C is shown. The length of

Question

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Triangle ABC is a sketch of a triangular flower bed that has an area of 65.1 square feet. Triangle A B C is shown. The length of

A B is 13 feet, the length of B C is 10 ft, and the length of A C is b. Angle B C A is 50 degrees. Trigonometric area formula: Area = One-half a b sine (C) To the nearest foot, what amount of fencing is needed to surround the perimeter of the flower bed? 17 feet 33 feet 40 feet 50 feet

Mathematics

2 answers:

Mazyrski [523] · Answer 1 · 2022-09-29T15:48:22+03:00

Answer:

40 feet

Step-by-step explanation:

A triangle is a polygon with three sides and three angles. There are different types of triangles such as isosceles triangle, equilateral triangle, scalene triangle, right angled triangle.

The area of triangle ABC is given as:

Area = (1/2) * AC * BC * sin(C)

But C = 50°, Area = 65.1 ft², BC = 10 ft, AC = b, AB = 13 feet.

Substituting gives:

65.1 = (1/2) * b * 10 * sin(50)

3.83b = 65.1

b = 17 ft

Perimeter of ΔABC = AB + AC + BC = 17 + 13 + 10

Perimeter of ΔABC = 40 feet