Question

A tree is 4 ft 2 in. Tall. To find the height of a tower, the shadow of the tree and the shadow of the tower were measured. What is the height h of the tower?.

Answer 1

Answer:

20 ft

Step-by-step explanation:

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

ZY=(24⋅12) in.

Simplify.

ZY=288 in.

RH=(4⋅12) in.+2 in.

Simplify.

RH=50 in.

RQ=(5⋅12) in.

Simplify.

RQ=60 in.

ZX¯¯¯¯¯ and QH¯¯¯¯¯¯ are parallel because the rays of the Sun that form them are parallel. Therefore, the angles they form with the ground

are congruent: ∠Z≅∠Q.  

∠Y≅∠R by the Right Angle Congruence Theorem.

Therefore, by the Angle-Angle Similarity △ZXY~△QHR.

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

ZYQR=XYHR

Substitute the values.

28860=h50

Cross multiply.

60h=50(288)

Simplify.

60h=14400

Divide both sides by 60.

h=240

The height of the tower is 240 in., or 20 ft.