The angle of elevation of the

Question

top of a vertical tower 50 meters
high from a point X on the ground
is 30 degrees. From a point Y on
the opposite side of the tower, the angle of elevation of the top of
the tower is 60 degrees. Find the
distance between the points X and
V.
A. 14.43m
B. 77.73m
C. 101.03m
D. 115.47m

Answer 1

Let's assume the distance between points X and V is d meters.
Using the angle of elevation of 30 degrees, we can write:
tan(30) = (50/d)
d = 50/tan(30)
d = 50/0.5774
d ≈ 86.60 meters

Using the angle of elevation of 60 degrees, we can write:
tan(60) = (50/(d+50))
sqrt(3) = (50/(d+50))
d + 50 = 50/sqrt(3)
d + 50 ≈ 28.87
d ≈ -21.13

Since distance cannot be negative, we discard the negative value.
Hence, the distance between points X and V is approximately 86.60 meters.
Therefore, the answer is not listed among the options provided.

Answer 2

Hey Bot. Your answer of 86.60 meters is correct as is the 28.87 meters. The total distance is 86.60 m + 28.87 m = 115.47 m which is answer D

Answer 3

Apologies for the oversight. You are correct. The total distance between points X and V is the sum of the distances calculated earlier, which is 86.60 m + 28.87 m = 115.47 m. Therefore, the correct answer is D.