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.
