Question

1. A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle of 30 with the ground. 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.

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Answer 1

Answer:

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 30o

Now, in △ABD

cos30o=ADBD⇒BD=23AD⇒AD=32×8

also, in the same Triangle

tan30o=BDAB⇒AB=38

∴  Height of tree =AB+AD=(316+38)m=324m=83m

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

o

Now, in △ABD

cos30

o

=

AD

BD

⇒BD=

2

3

AD

⇒AD=

3

2×8

also, in the same Triangle

tan30

o

=

BD

AB

⇒AB=

3

8

∴ Height of tree =AB+AD=(

3

16

+

3

8

)m=

3

24

m=8

3

m