Question

The tips of the shadows of a tree and of a metre stick meet at a point X. the following measurements are taken:

XS = 3.5m
ES = 6.5m
Use this information to find the height of the tree, to the nearest tenth of a metre.
attachment:

Answer 1

The height of tree is 2.8 m

Explanation:

Given : TE = height of tree

MS = meter stick

XS = 3.5 m

ES = 6.5 m

Solution : In ΔXMS and ΔXTE

∠MXS=∠TXE (common angle) ---1

∠XMS=∠XTE ---2

Reason : Correspoding angles are equal . since MS is parallel to TE so ∠XMS and ∠XTE will be corresponding angles

∠XSM =∠XET = 90° ---3

So, by 1 , 2 and 3 ΔXMS and ΔXTE are similar triangles by AAA property.

Since they are similar and we know that two triangles have their corresponding angles equal if and only if their corresponding sides are proportional.

⇒
`(XS)/(XE) =(MS)/(TE)`

⇒
`(3.5)/(10) =(1)/(TE)`

⇒
`TE =(1*10)/(3.5)`

⇒
`TE =2.8`

Thus The height of tree is 2.8 m