Question

hey mate answer fast it's urgent

Answer 1

hey mate. here is ur answer . plz mark it as brainlist.

Answer 2

As the question is to find the Actual Height of the Tree, We need to find the Length of the Broken part of the Tree and Length of the Remaining part of the Tree which is standing and then add both these Lengths to get the Actual Height of the Tree.

So, How to find these Lengths?

First of all : Let us draw the Figure which represents the Problem's Situation, So that we may get some idea to solve the Problem.

As the Broken part of the Tree touches the ground at some distance away from the foot of the Tree : The Remaining part of the Tree which is standing - The Broken part of the Tree - Distance between Foot of the Tree and the point where the Broken part touches the Ground make up a Triangle.

Let the Broken part of the Tree be : RP

Let the Remaining part of the Tree which is standing be : TR

Let the Distance between the Foot of the Tree and point where the Broken part touches the Ground be : TP

From the Figure, We can Notice that :

✿  TR is the Opposite Side of the Triangle

✿  RP is the Hypotenuse of the Triangle

✿  TP is the Adjacent Side of the Triangle

We know that :

✿  $\sf{Tangent\;of\;a\;Triangle = \dfrac{Opposite\;Side\;of\;the\;Triangle}{Adjacent\;Side\;of\;the\;Triangle}}$

$\sf{\implies Tangent(30) = \dfrac{TR}{TP}}$

$\sf{\implies \dfrac{1}{\sqrt{3}} = \dfrac{TR}{30}}$

$\sf{\implies TR= \dfrac{30}{\sqrt{3}}}$

$\sf{\implies TR= {10}{\sqrt{3}}$

$\sf{\implies TR = 17.32\;Meter}$

We know that :

✿  $\sf{Cosine\;of\;a\;Triangle = \dfrac{Adjacent\;Side\;of\;the\;Triangle}{Hypotenuse\;of\;the\;Triangle}}$

$\sf{\implies Cosine(30) = \dfrac{TP}{RP}}$

$\sf{\implies \dfrac{\sqrt{3}}{2} = \dfrac{30}{RP}}$

$\sf{\implies \dfrac{1}{2} = \dfrac{10\sqrt{3}}{RP}}$

$\sf{\implies \dfrac{1}{2} = \dfrac{17.32}{RP}}$

$\implies \sf{RP = 17.32 \times 2}$

$\implies \sf{RP = 34.64\;Meter}$

✿  $\textsf{Actual Height of the Tree = TR + RP}$

$\implies \textsf{Actual Height of the Tree = (17.32 + 34.64)\;Meter}$

$\implies \textsf{Actual Height of the Tree = 51.96\;Meter}$

$\implies \textsf{Actual Height of the Tree = 52\;Meter\;(Approx)}$