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 = 13, b = 4, c = 34
A) $15$ ft
B) $8$ ft
C) $10 \frac { 6 } { 13 } \mathrm { ft }$
D) $7 \frac { 6 } { 13 } \mathrm { ft }$

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 = 13, b = 4, c = 34
A) $15$ ft 
B) $8$ ft 
C) $10 \frac { 6 } { 13 } \mathrm { ft }$ 
D) $7 \frac { 6 } { 13 } \mathrm { ft }$

Quizplus · Accepted Answer

Using similar triangles, we can set up the proportion:

$$\frac{h}{13}=\frac{h+4}{34}$$

Cross-multiplying and simplifying, we get:

$$34h=13h+52$$

$$21h=52$$

$$h=\frac{52}{21}=2\frac{10}{21} \approx 10.57$$

So the height of the flagpole is about 10.57 feet, which is closest to choice C, 10 6/13 ft.

Use Similar Triangles to Help Solve the Problem 151515 Ft B) 888

Use Similar Triangles to Help Solve the Problem $15$ Ft
B) $8$