Question

A tree is broken by wind . The top of the tree struck the ground at an angle of 45 degrees and at a distance of 10 metres from the root, then the whole height of the tree is ​

Answer 1

Step-by-step explanation:

Segment AB represents the height of the tree.

The tree breaks at point D.

∴ Segment AD is the broken part of tree which then takes the position of DC.

∴AD=DC

Given m∠DCB=30∘,BC=30m

In right angled ΔDBC,

tan30∘=BCBD

⇒31=30BD

⇒BD=330

∴BD=103m

Also cos30∘=DCBC

⇒23=DC30

⇒DC=360

∴DC=203m

Hence AD=DC=203m

From the figure, AB=AD+DB

∴AB=203+103

⇒AB=303m

∴AB=30×1.73

∴AB=51.9m

Hence, the height of tree is 51.9m.