Question

A vertical pole of length 8 m casts a shadow 6 cm long on the ground and at the same time a tower casts a shadow 30 m long. Find the height of tower

Answer 1

Answer:

Bookmark

A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

1375131

Expand-image

Medium

Answer

Height of pole=AB=6 m

Length of shadow of pole =BC=4 m

Length of shadow of tower=EF=28 m

In △ABC and △DEF

∠B=∠E=90

∘

both 90

∘

as both are vertical to ground

∠C=∠F (same elevation in both the cases as both shadows are cast at the same time)

∴△ABC∼△DEF by AA similarity criterion

We know that if two triangles are similar, ratio of their sides are in proportion

So,

DE

AB

=

EF

BC

⇒

DE

6

=

28

4

⇒DE=6×7=42 m

Hence the height of the tower is 42 m

Answer 2

Answer:

The height of the tower is 40 m

Step-by-step explanation:

Given:

• Height of the pole is 8 m
• Length of the shadow is 6 m
• Length of shadow of tower is 30 m

To find: Height of the tower

Solution:

Height of the pole = AB = 8 m

Length of shadow of pole = BC = 6 m

Length of shadow of tower = EF = 30 m

The triangle ABC and DEF are given below

In ΔABC and ΔDEF

∠B = ∠E = 90

Both are 90 as both are vertical to ground

∠c = ∠f

Therefore same elevation in both the cases as both shadows are cast at the same time.

According to the AA similarity criterion

ΔABC ≈ ΔDEF

We know that if two triangles are similar ratio of their are in proportion.

Therefore

$\frac{AB}{DE} = \frac{BC}{EF}$

⇒ $\frac{8}{DE} = \frac{6}{30}$

⇒ DE = 8 × 5

⇒ DE = 40 m

Final answer:

The height of the tower is 40 m

#SPJ3