Question

A 96-ft high transmission tower casts a 72-ft long shadow. An anchor wire runs from the top of the tower to the tip of the shadow. A ladder is set up vertically 66 feet from the base of the tower so the top of the ladder touches the wire. What is the height of the ladder?

A. 6ft
B. 8ft
C. 10ft
D. 12ft

Answer 1

See attached picture and check solution below.
We are given with the following values:
A = length of transmission line = 96ft
B = length of shadow = 72 feet
C = distance of ladder to base of transmission line = 66 feet

Solve for angle created between the wire and tip of the shadow:
tan x = opposite/ adjacent
tan x = 96 feet / 72 feet
x = 53.13°

Solving for the height of the ladder:
tan x = Ladder length / (72-66)
tan 53.13° * (72-66) = ladder length
ladder length = 8 feet

The answer is letter "B" which is 8 feet.