Answer: a) 2 miles
b) 4 miles
Explanation:
There are two right angle triangles formed in the rectangle.
Taking 30 degrees as the reference angle, the length of the side walk, h represents the hypotenuse of the right angle triangle.
The width, w of the park represents the opposite side of the right angle triangle.
The length of the park represents the adjacent side of the right angle triangle.
a) to determine the width of the park w, we would apply
the tangent trigonometric ratio.
Tan θ, = opposite side/adjacent side. Therefore,
Tan 30 = w/2√3
1/√3 = w/2√3
w = 1/√3 × 2√3
w = 2
b) to determine the the length of the side walk h, we would apply
the Cosine trigonometric ratio.
Cos θ, = adjacent side/hypotenuse. Therefore,
Cos 30 = 2√3/h
√3/2 = 2√3/h
h = 2√3 × 2/√3
h = 4