73.6k views
2 votes
Tom is 5 ft 6 in. tall. To find the height of a building, he measured his shadow and the building's shadow. What is the height h of the building? HELP ASAP!

Tom is 5 ft 6 in. tall. To find the height of a building, he measured his shadow and-example-1
User ZooKeeper
by
8.7k points

2 Answers

4 votes

Answer:44 ft

Explanation:

Convert all measurements to a single unit, inches, using the fact that 1 foot is equal to 12 inches.

MN=(26⋅12) in.

Simplify.

MN=312 in.

QR=(3⋅12) in.+3 in.

Simplify.

QR=39 in.

PQ=(5⋅12) in.+6 in.

Simplify.

PQ=66 in.

LN and PR are parallel because the rays of the Sun that form them are parallel. Therefore, the angles they form with the ground

are congruent: ∠N≅∠R

∠M≅∠Q by the Right Angle Congruence Theorem.

Therefore, by the Angle-Angle Similarity △LMN~△PQR

Find LM . Set up a proportion with the lengths of the known sides and the unknown length (height of the building).

PQ/QR=LM/MN

Substitute the values.

66/39=h/312

Cross multiply.

39h=66(312)

Simplify.

39h=20592

Divide both sides by 39 .

h=528

Therefore, the height of the building is 528 in., or 44 ft.

User CocoNess
by
8.6k points
4 votes

I believe your answer would be 44 ft. I could be wrong, but I got 26 ft/3 ft 3 in = 8. 5 ft 6in × 8 = 44 ft.

User Maxadorable
by
8.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories