Suppose light pole is at PQ.
Jesse is at RS.
Mirror is at M.
In the diagram; PQ = h, QM = 25 feet, RS = 6 feet, SM = 5.5 feet.
We know angle of incidence = angle of reflection, so ∠i = ∠r.
It means ∠x = ∠a
and 90-x = 90-a ⇒ ∠y = ∠b
∠Q = ∠S = 90°
It means triangle ΔPQM is similar to triangle ΔRSM.
So, Ratio of corresponding sides would be proportional.
[tex]\frac{PQ}{QM} =\frac{RS}{SM} \\\frac{h}{25} =\frac{6}{5.5} \\Using \;Cross \;Multiplication\\5.5*h = 25*6\\5.5h = 150\\Dividing \;both \;sides \;by \;5.5\\\frac{5.5h}{5.5} =\frac{150}{5.5} \\h = \frac{1500}{55} \\h = \frac{300}{11} =27.27272727 \approx 27.3 \;feet[/tex]
Hence, the height of the light pole is 27.3 feet.
