The antenna's height is approximately 17.43 feet, calculated using the tangent function and the given angle α. The distance to Anchor 2 from the base of the antenna is approximately 43.68 feet, calculated using the antenna's height and tangent function with the given angle β.
Step-by-step explanation:
To determine the height of the antenna, we use the trigonometric function tangent since we have the opposite side (height of the antenna) and the adjacent side (distance from the base to Anchor 1). The angle given is α = 16.62 degrees, and the distance to Anchor 1 is 58 feet.
The tangent of α is equal to the opposite side (height) divided by the adjacent side (58 feet).
tan(α) = height / 58 feet
height = 58 feet * tan(16.62 degrees)
We calculate the height:
height = 58 feet * tan(16.62°)
Computing this we get,
height ≈ 58 feet * 0.3005 ≈ 17.43 feet
For the distance to Anchor 2, we use the height found in part (a) and angle β = 21.77 degrees. By using tangent again:
tan(β) = height / distance to Anchor 2
distance to Anchor 2 = height / tan(β)
Computing this we get,
distance to Anchor 2 ≈ 17.43 feet / tan(21.77°) ≈ 17.43 feet / 0.3992 ≈ 43.68 feet