A tree leaned due to storm. The pole with height of 7
metre from its foot was leaned against the tree to
make it straight. If the angle of depression at the
point of contacting the pole on the ground is 30°,
then what is the length of the pole?
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NOTE: Question posted is slightly incorrect and we have to find the height of the tree (NOT the pole), since height of the pole is already given.
GIVEN:
Height of the pole = 7 metres, Angle of depression = 30⁰
ANSWER:
Height of the tree is 3.5 metres
SOLUTION:
(Refer the diagram in the attachment)
In triangle ABC,
AB = Height of the tree,
AC = Height of pole = 7 metres
∠ABC = 90⁰
Angle of depression = 30⁰
==> ∠ACB = 30⁰
---------------------------------------------->
Sin 30⁰ = Opposite side/Hypotenuse
= AB/AC
==> 1/2 = AB/7
==> AB = 7/2 = 3.5
∴ Height of tree is 3.5 metres ✅
Attachments:
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