Final answer:
To calculate the horizontal distance from the tower to the stake, one can use the tangent of the angle of depression, which relates to the opposite side (height of the tower) and the adjacent side (distance needed). After applying trigonometric functions, the answer is found to be 45 feet.
Step-by-step explanation:
The question involves using trigonometry to find the horizontal distance from the foot of a tower to a stake on the ground when given the angle of depression and the height of the tower. To solve this, one can use the tangent function (tan) because it relates the angle of depression to the opposite side (height of the tower) and the adjacent side (distance from the tower we need to find).
The tangent of an angle in a right-angled triangle equals the opposite side divided by the adjacent side. In this case:
tan(52°) = opposite/adjacent
Substituting the given values:
tan(52°) = 60 feet / distance
To find the distance, we rearrange the equation and solve for the adjacent side:
distance = 60 feet / tan(52°)
Using a calculator, this gives us the distance. The correct answer is (b) 45 feet, as this is the horizontal distance from the foot of the tower to the stake when calculated using the tangent function with the given angle of depression and height.