Question

Joseph is standing 12 feet from a mirror lying on the ground, and his eyes are 5 feet above the ground. The line-of-sight reflections on the mirror makes mc003-2.jpg congruent to mc003-3.jpg . If the building is 264 feet from the mirror, which is closest to the height of the building?

Answer 1

See the attached figure which represents the explanation of the problem.
Let the height of the building = h

∵ ∠1 congruent to ∠2
∴ ∠1 = ∠2
∴ tan (∠1) = tan (∠2)    ⇒⇒⇒  tan of the angle =  (opposite/adjacent)

∴ $\frac{5}{12} = \frac{h}{264}$
∴ 12 h = 5 * 264 = 1,320
∴ h = 1,320/12 = 110 feet

∴ The height of the building = 110 feet