Answer

Verified

340.8k+ views

**Hint:**This problem is from heights and distances. We will easily solve this just by applying \[{30^ \circ } - {60^ \circ } - {90^ \circ }\] triangle theorem. That is side opposite to \[{60^ \circ }\] is \[{{{\sqrt 3 }} \!{\left/

{\vphantom {{\sqrt 3 } 2}}\right.}

\!\lower0.7ex{2}}\] times the hypotenuse and that opposite to \[{30^ \circ }\] is half of the hypotenuse. This is the simple and correct approach we will use here only because we know the angle of elevation.

**Step by step solution:**

Now let’s draw the figure first with a tower of height supposed to say h and the angle of elevation is \[{30^ \circ }\]. Also given that the distance is 300 meters from its foot on a horizontal plane.

This is the figure so formed. Now we will find the height of the tower with the help of hypotenuse of the figure.

Using our \[{30^ \circ } - {60^ \circ } - {90^ \circ }\] triangle theorem,

Side opposite to \[{60^ \circ }\]=300

\[ \Rightarrow {{{\sqrt 3 }} \!{\left/

{\vphantom {{\sqrt 3 } 2}}\right.}

\!\lower0.7ex{2}} \times hypt = 300\]

Thus value of hypotenuse is

\[ \Rightarrow hypt = 300 \times {{2} \!{\left/

{\vphantom {2 {\sqrt 3 }}}\right.}

\!\lower0.7ex{{\sqrt 3 }}}\]

Thus we get, \[ \Rightarrow hypt = {{{600}} \!{\left/

{\vphantom {{600} {\sqrt 3 }}}\right.}

\!\lower0.7ex{{\sqrt 3 }}}m\]

Now to get the height of the tower we will use this hypotenuse length.

Height of the tower is exactly the side opposite to the elevation angle \[{30^ \circ }\].

Side opposite to \[{30^ \circ }\]= \[{{1} \!{\left/

{\vphantom {1 2}}\right.}

\!\lower0.7ex{2}} \times hypt\]

\[ \Rightarrow h = {{1} \!{\left/

{\vphantom {1 2}}\right.}

\!\lower0.7ex{2}} \times hypt\]

Putting the value of hypotenuse

\[ \Rightarrow h = {{1} \!{\left/

{\vphantom {1 2}}\right.}

\!\lower0.7ex{2}} \times {{{600}} \!{\left/

{\vphantom {{600} {\sqrt 3 }}}\right.}

\!\lower0.7ex{{\sqrt 3 }}}\]

\[ \Rightarrow h = {{{300}} \!{\left/

{\vphantom {{300} {\sqrt 3 }}}\right.}

\!\lower0.7ex{{\sqrt 3 }}}m\]

This is the height of the tower \[ \Rightarrow h = {{{300}} \!{\left/

{\vphantom {{300} {\sqrt 3 }}}\right.}

\!\lower0.7ex{{\sqrt 3 }}}m\]

**But there is no option matching here. Thus option D is the correct option “none of these”.**

**Note:**

Students don’t hurry when you choose options because most of the students find the correct answer but fail to select. See here in this case the answer is in ratio form but since option B is similar looking people may tick it as correct. But it is the wrong one. So be careful when you choose the option.

Recently Updated Pages

The branch of science which deals with nature and natural class 10 physics CBSE

Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference Between Plant Cell and Animal Cell

Give simple chemical tests to distinguish between the class 12 chemistry CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

How will you bring about the following conversions class 12 chemistry CBSE

Consider a system of two identical particles One of class 11 physics CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

State the laws of reflection of light