Answer:
Step-by-step explanation:
In the figure attached, A is the peak of mountain AB, ED is Tyler who is 6 feet high.
Mirror placed at C, is 20 feet from the base of peak. Tyler is 3 feet away from the mirror.
1). When Tyler sees the peak in the mirror, angle of incidence " i " and angle of reflection " r " made by incident ray AC and reflected ray EC will be equal.
Now we can easily say ∠ r = ∠ E ( Alternate angles )
∠ i = ∠ A ( alternate angles)
Since ∠ i = ∠ r
Therefore, ∠ A = ∠ E
∠B = ∠D = 90°
and ∠ACB = ∠ECD
Hence ΔABC is similar to ΔCDE.
2). Corresponding sides of these similar triangles are AB and ED, BC and CD, AC and CE.
3). tanE = [tex]\frac{CD}{DE}=\frac{3}{6}[/tex]
tanE = 0.5
∠ E = [tex]tan^{-1}(0.5)=26.57[/tex] degrees
Now ∠E = ∠A = 26.57°
Therefore, tan(26.57) = [tex]\frac{20}{AB}[/tex]
0.5 = [tex]\frac{20}{AB}[/tex]
AB = [tex]\frac{20}{0.5}=40[/tex]
Therefore, height of the peak AB is 40 feet.
