A vertical straight tree 12m high is broken by strong wind in such way that top touches the ground and makes an angle of 30° with the ground. Find at what height from the ground did the tree break.
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Step-by-step explanation:
Height of the = AC+BC=12m
Let AC=xm
In ΔABC,
sin60
∘
=
12−x
x
2
3
=
12−x
x
3
(12−x)=2x
12
3
−
3
x=2x
∴12
3
=2x+
3
x
=x(2+
3
)
2+
3
12
3
=x
(2+
3
)(2−
3
)
(12
3
)(2−
3
)
=x
4−3
(12
3
)(2−
3
)
=x
12
3
(2)−12×3=x
24
3
−36=x
24×1.73−36=x (
3
=1.73)
41.52−36=x
∴x=5.52m
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