Question

21. A vertical row of trees 20 m long casts a shadow 16 m long on the ground. At the same time a tower
casts the shadow 48 m long on the ground.
(1) Determine the height of the tower
fit) Which mathematical concept is used in this problem?​

Answer 1

(i) The height of the tower would be 60 m

(ii) Similar Triangles

Step-by-step explanation:

Consider AB represents the height of tree and AC represents its shadow height while, PQ represents the tower and PR represents the shadow of tower ( shown in below diagram ),

In triangles ABC and PQR,

∠A ≅ ∠ P    ( right angles ),

∠C ≅ ∠R      ( Cast angles by sun at same time are same )

By AA similarity postulate,

$\triangle ABC\sim \triangle PQR$

Since, the corresponding sides of similar triangles are in same proportion,

$\implies \frac{AB}{AC}=\frac{PQ}{PR}$

If AB = 20 m, AC = 16 m and PR = 48 m,

$\frac{20}{16}=\frac{PQ}{48}$

$\frac{5}{4}\times 48=PQ$

$5\times 12 = PQ$

$\implies PQ =60\text{ m}$

Hence, the height of the tower would be 60 meters.

And, the similar triangles concept used in solving the question.

#Learn more:

A vertical pole 40 m long cast a shadow 20 m long on the ground. Find the  height of the tower that casts a shadow 50 m long on the ground at the same  time.​

https://brainly.in/question/14648036