a tree broken by the wind touches the ground at a distance of 10 metres from the foot of the tree if the height of the tree is 30 metres and that of the broken portion 20 metres then angle which the broken part makes with the ground is
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10th
Maths
Some Applications of Trigonometry
Heights and Distances
A vertical tree is broken b...
MATHS
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Asked on December 26, 2019 by
Anabhra Dhamodharan
A vertical tree is broken by the wind. The top of the tree touches the ground and
makes an angle 30
∘
with it. If the top of the tree touches the ground 30m away from its foot, then find the actual height of the tree.
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ANSWER
Let C be the point at which the tree is broken and let the top of the tree touch the ground at A.
Let B denote the foot of the tree.
Given AB=30m and ∠CAB=30
∘
In the right angled △CAB,
tan30
∘
=
AB
BC
⇒BC=ABtan30
∘
∴BC=
3
30
=10
3
m (1)
Now, cos30
∘
=
AC
AB
⇒AC=
cos30
∘
AB
So,
AC=
3
30×2
=10
3
×2=20
3
m. (2)
Thus, the height of the tree =BC+AC=10
3
+20
3
=30
3
m.
solution
Answer:
63.43°
Step-by-step explanation:
The height of the tree trunk left is 20, and the point where it touches the ground is 10.
Let the angle made by base & the broken portion of the tree be Ф
TanФ = 20/10 = 2
Ф = tan⁻¹ 2 = 63.43°
as shown in the attachment
