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

Ok, what you have there is two similar triangles (the sides have the same proportions in each). The bigger triangle is
(6.5+3.5)/3.5≈2.857
times bigger than the smaller one. So the height of the tree which is parallel to the metre stick is approx. 2.857 times bigger than the metre stick. So the height of the tree is 2.9 m (1 d.p).

Answer 2

Answer:

The height of tree is 2.8 m

Step-by-step 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.

⇒$\frac{XS}{XE} =\frac{MS}{TE}$

⇒$\frac{3.5}{10} =\frac{1}{TE}$

⇒$TE =\frac{1*10}{3.5}$

⇒$TE =2.8$

Thus The height of tree is 2.8 m