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:
What is the height of the house? Show your work and explain your reasoning in complete sentences.

Answer 1

What is the height of the house? Show your work and explain your reasoning in complete sentences.

Answer 2

I got 18.75...???

Answer 3

h/15 = 5/4

your answer is correct

Answer 4

Thank you!

Answer 5

Is my reasoning okay:
The height of the house is 18.75. I got this using the property of similar triangles and the pythagorean theorem. The height of the smaller triangle is 5 because of the height of Annie while the length is 4 because of the mirror on the ground. Since she is 15 feet away from the house, the base of the larger triangle is 15. The pythagorean theorem states if a right triangle has sides a and b and hypotenuse c then a^2 + b^2 = c^2. 5/4 = 1.25. 1.25*15 = 18.75.

Answer 6

@MrNood

Answer 7

No - your reasoning is not entirely correct.

The answer is simply based in similar triangles

both triangles have a right angle and both have the same angle of relection at th emirror (due to properties of reflection0 . therfore the 3rd angle is also the sam in both trianglaes (since all triangles add to 180 deg)

So th angle at the mirror from the viewer is tan^-1 5/4 as you said

The base of the large triangle is 15 and the wall is h

the other angle at the mirror is ALSO tan^-1 5/4 but you can see it is tan^-1 h/15

therefore h/15 = 5/4

You would only need pythagoras to find the 'hypotenuse' - that is the distance from the roof to the mirror, or the distance from eyes to mirror.