Question

A vertical pole is 6 m high . It casts a shadow 9 cm long at the same time that a tree casts a shadow 30 cm long. Find the height of the tree.

Answer 1

Answer:

20 m

Step-by-step explanation:

Let the angle of elevation of sun be $\theta$

Then in the case of pole the pole is perpendicular to the ground thus if we consider the pole and length of shadow to be the 2 arms of a right triangle it forms a right triangle.

Here,

$Perpendicular = Pole = 6 m = 600cm\\Base = Shadow = 9 cm\\Now\\ tan(\theta) = \frac{Perpendicular}{Base} = \frac{600}{9} = \frac{200}{3}$

For the tree also the angle of elevation of sun will remain the same as the measurements are taken at the same time.

Then in the case of tree the tree is perpendicular to the ground thus if we consider the tree and length of shadow to be the 2 arms of a right triangle it forms a right triangle.

Here,

$Perpendicular = Tree = x\\Base = Shadow = 30 cm\\Now\\ tan(\theta) = \frac{Perpendicular}{Base} = \frac{x}{30}\\From \ above \ we \ know \ that\\tan(\theta) = \frac{200}{3}\\Therefore,\\\frac{x}{30} = \frac{200}{3}\\3x = 6000\\x = \frac{6000}{3} = 2000 \ cm = 20 \ m$

Therefore Height of tree is 20 m