Use similar triangles to help solve the problem. A man places a mirror on the ground and sees the reflection of the top of a flagpole as shown in the figure below. The two triangles in the figure are similar. Find the height h of the flagpole. a = 11, b = 7, c = 31
A) $14$ ft
B) $21$ ft
C) $19 \frac { 8 } { 11 } \mathrm { ft }$
D) $22 \frac { 8 } { 11 } \mathrm { ft }$

Question

Use similar triangles to help solve the problem. A man places a mirror on the ground and sees the reflection of the top of a flagpole as shown in the figure below. The two triangles in the figure are similar. Find the height h of the flagpole.  a = 11, b = 7, c = 31
A) $14$ ft 
B) $21$ ft 
C) $19 \frac { 8 } { 11 } \mathrm { ft }$ 
D) $22 \frac { 8 } { 11 } \mathrm { ft }$

Quizplus · Accepted Answer

Using similar triangles, we have:
$\frac{a}{h}=\frac{b}{x}$
$\frac{a+b}{h+x}=\frac{c}{x}$
Substituting the given values, we get:
$\frac{11}{h}=\frac{7}{x}$
$\frac{11+7}{h+x}=\frac{31}{x}$
Solving for $x$ in the first equation, we get $x=\frac{7h}{11}$
Substituting this value in the second equation and simplifying, we get:
$h = \frac{231}{121} \mathrm{ft}$ or $h \approx 1.909 \mathrm{ft}$
Therefore, the best choice is C, $19 \frac { 8 } { 11 } \mathrm { ft }$.

Use Similar Triangles to Help Solve the Problem 141414 Ft B) 212121

Use Similar Triangles to Help Solve the Problem $14$ Ft
B) $21$