Math, asked by sathwikdunaboina, 11 months ago

32 The angles of depression and elevation of the top of a wall 11 m high from top and bottom of a tree are 60° and 30°
respectively. What is the height of the tree?​

Answers

Answered by pinky162
7

Step-by-step explanation:

i hope this is help you..

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Answered by yogeshkumar49685
0

Concept:

The term "angle of elevation" refers to the angle that exists between the horizontal and an object. The line of sight of an observer would be above the horizontal. The term "angle of depression" refers to the downward angle from the horizontal to an item. The line of sight of an observer would be below the horizontal.

Given:

The height of the wall is 11m.

The angle of elevation and depression is 30{\°}, 60^{\°} respectively.

To Find:

Height of tree

Solution:

Let AB be the tree and DC be the wall.

It is given that  $\angle \mathrm{DBC}=30^{\circ}, \angle \mathrm{DAE}=60^{\circ}, \mathrm{DC}=11 \mathrm{~m}$.

Find side BC.

\begin{aligned}&\tan 30^{\circ}=\frac{D C}{B C} \\&\frac{1}{\sqrt{3}}=\frac{11}{B C} \\&B C=11 \sqrt{3} m \\&A E=B C=11 \sqrt{3} m\end{aligned}

Find value of ED

\begin{aligned}\tan 60^{\circ} &=\frac{E D}{A E} \\\sqrt{3} &=\frac{E D}{11 \sqrt{3}}[\because \text { Use value of AE from equation 1 }] \\E D &=11 \sqrt{3} \times \sqrt{3} \\&=11 \times 3 \\&=33\end{aligned}

Find the height of the tree $=A B\\

AB=EC=ED+DC\\$=33+11$\\$=44 \mathrm{~m}$

Therefore the height of the tree is 44m.

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