Question

A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it.The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.​

Answer 1

Answer:

10th

Maths

Some Applications of Trigonometry

Heights and Distances

A tree breaks due to storm ...

MATHS

Asked on November 22, 2019 byAditya Panchal

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 30o with the ground. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.

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=3

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