Answer :
Final answer:
Using trigonometry and the given angle of 62 degrees with a 95-foot shadow, the height of the radio tower is calculated to be 178.6665 feet. The correct answer is B).
Explanation:
To find the height of a radio tower when a 95-foot shadow is cast by the sun and the angle from the tip of the shadow to the top of the tower is 62 degrees, we use trigonometry.
Specifically, the tangent function (tan) in a right-angled triangle, where the tangent of an angle is the ratio of the opposite side (height of the tower) to the adjacent side (length of the shadow).
Using the given information, θ = 62°, and length of the shadow = 95 feet,
tan(62°) = Height of the tower / 95
Using a calculator to find tan(62°), we get approximately 1.8807. Therefore,
1.8807 = Height of the tower / 95
Height of the tower = 95 × 1.8807
Height of the tower = 178.6665 feet
Thus, the height of the radio tower, rounded to four decimal places, is 178.6665 feet.
