a tree stands vertically on a hill side which makes an angle of 15degree with the horizontal from a - Maths - Trigonometric Functions

Question

a tree stands vertically on a hill side which makes an angle of
15degree with the horizontal from a point on the ground 35m down
the hill from the base of the tree, the angle of elevation of the
top of the tree is 60degree find the height of the tree
ans(35root2m) plese tell the xact solution

Aakash Sharma · Accepted Answer

Let PQ be tree and A be the point on ground

AR such that AP = 35 m

Now ∠QAR = 60° and ∠PAR = 15°

⇒∠PAQ = ∠QAR – ∠PAR = 60° – 15° = 45°

⇒∠AQP = 90° – ∠QAR = 90° – 60° = 30°

Using such rule we get

$\frac{AP}{\sin 30 °} = \frac{PQ}{\sin 45 °} \Rightarrow \frac{35}{\frac{1}{2}} = \frac{PQ}{\frac{1}{\sqrt{2}}} \Rightarrow PQ = 35 \sqrt{2} m$

Hence the required height of the tree is $35 \sqrt{2} m$ .

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a tree stands vertically on a hill side which makes an angle of 15degree with the horizontal. from a point on the ground 35m down the hill from the base of the tree, the angle of elevation of the top of the tree is 60degree. find the height of the tree. ans(35root2m) plese tell the xact solution

a tree stands vertically on a hill side which makes an angle of 15degree with the horizontal. from a point on the ground 35m down the hill from the base of the tree, the angle of elevation of the top of the tree is 60degree. find the height of the tree.

ans(35root2m) plese tell the xact solution