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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.
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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
o
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.
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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
Step-by-step explanation:
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Answer:
8√3 m.
Step-by-step explanation:
Height of the tree = AB + AC
Trigonometric ratio which involves AB, BC and ∠C is tan θ, where AB can be measured.
Trigonometric ratio which involves AB, AC and ∠C is sin θ, where AC can be measured.
Distance between the foot of the tree to the point where the top touches the ground = BC = 8 m
In triangle ABC,
tan C = AB / BC
tan 30° = AB / 8
1/√3 = AB / 8
AB = 8 / √3
sin C = AB / AC
sin 30° = (8/√3) / AC
1/2 = 8/√3 × 1 / AC
AC = 8/√3 × 2
AC = 16 / √3
Height of tree = AB + AC
= 8/√3 + 16/√3
= 24/√3
= 24 × √3 / √3 × √3. [On rationalizing ]
= (24√3) / 3
= 8√3
So, the height of tree is 8√3 meters.
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