Question

Annie walks 15 feet away from her house and places a mirror on the ground. She backs 4 feet away from the mirror so that she can see the tip of the roof. Annie's eyes are 5 feet above the ground. Annie and the house are both perpendicular to the ground. The angles between the top of the house, the mirror, and the ground and between Annie's eyes, the mirror, and the ground are congruent as shown in the image below: Image depicts a mirror on the ground between a person and a house. The mirror is 4 feet away from the person and 15 feet away from the house. What is the height of the house? Show your work and explain your reasoning in complete sentences.

Answer 1

Answer:

18.75 ft

Step-by-step explanation:

The given scenario can be drawn as shown in the following attachment.

Given that,

$m\angle DCE=\angle ACB$ and $m\angle DEC=\angle ABC=90^{\circ}$

Therefore, $\Delta ABC\sim \Delta DEC$

$\Rightarrow \dfrac{AB}{DE}=\dfrac{BC}{EC}$

$\Rightarrow \dfrac{AB}{5}=\dfrac{15}{4}$

$\Rightarrow AB=\dfrac{15\times 5}{4}=18.75$ ft

AB is the height of the house.

Answer 2

Answer:

The roof is 18.75 ft tall.

Step-by-step explanation:

You set up a proportion by taking the height of the house (x) divided by the height of her eyes (5) is equal to the distance between the mirror and the house (15) divided by the distance between her and the mirror (4).

Then you multiply each side by 5 to get x by itself which gives you 75/4 and you simplify that to get 18.75 ft.

heres what all of that looks like:

x/5 = 15/4

x = 5(15/4)

x = 75/4

x = 18.75