A
15 m high tree is broken by wind in such a way that its top touches the ground and makes
an angle 30° with the ground. At what height from the bottom the tree is broken by the wind.
Answers
Step-by-step explanation:
The height above the ground from the tree broke is 6.9 meter.
Step-by-step explanation:
Given : A vertically straight tree 15m high is broken by the wind in such a way that its top just touches the ground and makes an angle of 60 degree.
To find : At what height from the ground did the tree break ?
Solution :
The height of the tree = 15 m
Refer the attached figure below.
Suppose it broke at 'C' and its top 'A' touches the ground at 'D'
Now, AC = CD, and angle BDC = 60°
Let BC = 'x'
So, AC = 15 - x and CD = 15 - x
In right angle BCD,
\frac{BC}{CD}=\sin 60^\circ
CD
BC
=sin60
∘
\frac{x}{15-x}=\frac{\sqrt3}{2}
15−x
x
=
2
3
2x=(15-x)\sqrt32x=(15−x)
3
2x=15\sqrt3-\sqrt3 x2x=15
3
−
3
x
2x+\sqrt3 x=15\sqrt32x+
3
x=15
3
x(2+\sqrt3)=15\sqrt3x(2+
3
)=15
3
x=\frac{15\sqrt3}{(2+\sqrt3)}x=
(2+
3
)
15
3
x=\frac{25.98}{3.73}x=
3.73
25.98
x=6.96x=6.96
Therefore, The height above the ground from the tree broke is 6.9 meter.
