Question

A tree breaks due to storm and the broken part bends so that the top of the

tree touches the ground where it makes an angle 30° . The distance between

the foot of the tree to the point where the top touches the ground is 8m. Find

the height of the tree from where it is broken.​

Answer 1

tan30° = 8/x

1/√3 = 8/x

x= 8√3m

Answer 2

Answer:

Let the Height of the Tree =AB+AD

and given that BD=8 m

Now, when it breaks a part of it will remain perpendicular to the ground (AB) and remaining part (AD) will make an angle of 30.

now in ∆ABD

cos30=BD/AD

BD=root3AD/2

AD=2×8/root3

also, in the same Triangle

also, in the same Triangletan30

also, in the same Triangletan30 o

also, in the same Triangletan30 o =

also, in the same Triangletan30 o = BD

also, in the same Triangletan30 o = BDAB

also, in the same Triangletan30 o = BDAB

also, in the same Triangletan30 o = BDAB ⇒AB= 3

∴ Halso, in the same Triangle

also, in the same Triangletan30

also, in the same Triangletan30 o

also, in the same Triangletan30 o =

also, in the same Triangletan30 o = BD

also, in the same Triangletan30 o = BDAB

also, in the same Triangletan30 o = BDAB

also, in the same Triangletan30 o = BDAB ⇒AB= 3

∴ Height of tree =AB+AD=( 3)16+38)m=3 24

m=8

m=8 3

m=8 3

m=8 3 meight of tree =AB+AD=( 3)16+3 8)

m=3