Question

A city wanted to enclose a triangular portion of the city park to make a dog park. The triangular portion of the park that they are enclosing has sides of 280 ft., 190 ft., and 330 ft.In order to construct the fences correctly, the city wants to determine the angle between the 190 ft. Side and the 330 ft. Side. What is the approximate angle measure between the 190 ft. Side of the triangle and the 330 ft. Side of the triangle?

Answer 1

58 degrees

Explanation:

The diagram of the triangle ABC is shown in the attached photo. To determine the angles of the triangle, we will apply the cosine rule. The cosine rule states that

a^2 = b^2 + c^2 - 2bcCosA

From the diagram,

a = 280 ft

b = 190 ft

c = 330 ft

280^2 = 190^2 + 330^2 - 2×190×330CosA

78400 = 36100 + 108900 - 125400Cos A

78400 = 145000 - 125400Cos A

125400Cos A = 145000 - 78400

125400Cos A = 66600

CosA = 66600/125400

Cos A = 0.53

A = 58 degrees

Since we know one angle, we will apply the sine rule

a/sinA = b/sinB = c/sinC

280/sin58 = 190/sinB

Cross multiplying

280sinB = 190sin58

SinB = (190×0.8480)/280 = 0.575

B = 35 degrees.

Sum if angles in a triangle is 180 degrees. Therefore

C = 180 - 58 - 35 = 87 degrees

The approximate angle measure between the 190 ft side of the triangle and the 330 ft side is 58 degrees