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You place a mirror on the ground 6 feet from the lamppost. You move back 3 feet and see the top of the lamppost in the mirror. If you are 5 feet tall, what is the height of the lamppost?

Verified Answer :

JeanaShupp

Answer: 10 feet

Step-by-step explanation:

Let h be the height of lamppost.

Since both the person and the lamppost are standing vertical to the ground,  making similar right triangles.

Because the two triangles are similar, the ratio of their sides is the same.

Therefore, we have

\(\frac{\text{height of lamppost}}{\text{distance of lampost from mirror}}=\frac{\text{height of person}}{\text{distance of person from mirror}}\\\\\Rightarrow\frac{h}{6}=\frac{5}{3}\\\\\Rightarrow\ h=\frac{6\times5}{3}\\\\\Rightarrow\ h=10\)

Hence, the height of the lamppost = 10 feet.

fichoh

Setting up a proportional relationship between mirror and lamppost, the height of the lamppost is 10 feets.

  • Height of person, Hp = 5 feets

  • Distance of person form mirror, Dp = 3 feets

  • Distance of Lampost from mirror, Dm = 6 feets

  • Height of Lampost = Hl =?

Setting up a proportional relationship :

\(\frac{Hp}{Dp} = \frac{Hl}{Dm}\)

\(\frac{5}{3} = \frac{Hl}{6}\)

Cross multiply :

Hl × 3 = 6 × 5

3Hl = 30

Hl = (30 ÷ 3)

Hl = 10

Therefore, the height of the lamppost is 10 feets.

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