Question

(a) A vertical pole of height 10 m casts a shadow of 15 m on the ground and at the same time, a tower casts a shadow of 45 m on the ground. Find the height of the tower.

(b) In the given figure, $\frac{QR}{QS} = \frac{QT}{PR}$ and $∠1 = ∠2$ . Prove that $△ PQS \sim △ TQR$ .

Approach

Set up similar triangles for the pole and tower casting shadows at the same time. $\frac{10}{15} = \frac{h}{45}$ , so the height of the tower is $h = 30$ m.

Step-by-step working

1
$△ A BC \sim △ PQR$ (angle of elevation same), so $\frac{10}{15} = \frac{h}{45}$
1.5 marks
2
$h = 30$ m
0.5 marks

Concepts used

similar trianglesheight and distanceshadowsproportionalityprove

Approach

Step-by-step working

Concepts used

Similar question types