Define variables
Let:
- Distance from B to the base of the tower: x
- Distance from A to the base: x + 4.8
- Height of the tower above student's eye level: h
(so total tower height H = h + hs)
Use tangent for angle of elevation
From B: tan( B) = h / x => h = x * tan(64°)
From A: tan( A) = h / (x + 4.8) => h = (x + 4.8) * tan(69°)
Equate the two expressions for h
x * tan(64°) = (x + 4.8) * tan(69°)
x * (tan(64°) - tan(69°)) = 4.8 * tan(69°)
x = (4.8 * tan(69°)) / (tan(64°) - tan(69°))
Calculate values
tan(64°) = 2.0503, tan(69°) = 2.6051
x = (4.8 * 2.6051) / (2.0503 - 2.6051)
x 12.5045 / (-0.5548)
x = -22.54 m (ignore negative, distance = 22.54 m)
Find height above eye level
h = x * tan(64°) = 22.54 * 2.0503 = 46.2 m
Add student's eye level
H = h + hs = 46.2 + 1.5 = 47.7 m
Answer:
H = 47.7 m