The angle of elevation of a cloud <math><mi mathvariant="normal">C</mi></math> from a point <math><mi mathvariant="normal">P</mi><mo>,</mo><mn>200</mn><mtext></mtext><mi mathvariant="normal">m</mi></math> above a still take is <math><msup><mrow><mrow><mn>30</mn></mrow></mrow><mrow><mrow><mo>∘</mo></mrow></mrow></msup></math> . If the angle of depression of the image of <math><mi>C</mi></math> in the lake from the point <math><mi>P</mi></math> is <math><msup><mrow><mrow><mn>60</mn></mrow></mrow><mrow><mrow><mo>∘</mo></mrow></mrow></msup></math> , then <math><mi>P</mi><mi>C</mi></math> (in <math><mi mathvariant="normal">m</mi></math> ) is equal to

∑r=020?50-rC6=50C6+49C6+48C6+….+30C6=50C6+49C6+48C6+….+30C6+30C7-30C7=50C6+49C6+48C6+….+31C6+31C7-30C7=50C6+50C7-30C7=51C7-30C7

The angle of elevation of a cloud&nbsp;<math><mi mathvariant="normal">C</mi></math>&nbsp;from a point&nbsp;<math><mi mathvariant="normal">P</mi><mo>,</mo><mn>200</mn><mtext></mtext><mi mathvariant="normal">m</mi></math>&nbsp;above a still take is&nbsp;<math><msup><mrow><mrow><mn>30</mn></mrow></mrow><mrow><mrow><mo>∘</mo></mrow></mrow></msup></math>&nbsp;. If the angle of depression of the image of&nbsp;<math><mi>C</mi></math>&nbsp;in the lake from the point&nbsp;<math><mi>P</mi></math>&nbsp;is&nbsp;<math><msup><mrow><mrow><mn>60</mn></mrow></mrow><mrow><mrow><mo>∘</mo></mrow></mrow></msup></math>&nbsp;, then&nbsp;<math><mi>P</mi><mi>C</mi></math>&nbsp;(in&nbsp;<math><mi mathvariant="normal">m</mi></math>&nbsp;) is equal to

<math> <mn>400</mn> <mroot> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> <mrow></mrow> </mroot> </math> (Trigonometry)

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Maths NCERT Exemplar Solutions Class 12th Chapter Twelve Maths Class 12th Trigonometric Functions Maths NCERT Exemplar Solutions Class 12th Chapter Three

The angle of elevation of a cloud $C$ from a point $P, 200 m$ above a still take is $30^{\circ}$ . If the angle of depression of the image of $C$ in the lake from the point $P$ is $60^{\circ}$ , then $P C$ (in $m$ ) is equal to

Option 1 -

$200 \sqrt[]{3}$

Option 2 -

100

Option 3 -

400

Option 4 -

$400 \sqrt[]{3}$ (Trigonometry)

3 Views | Posted 2 months ago

Asked by Shiksha User

1 Answer

Answered by

alok kumar singh | Contributor-Level 10

2 months ago

Correct Option - 3

Detailed Solution:

$\sum_{r = 0}^{20} ?^{50 - r} C_{6} =^{50} C_{6} +^{49} C_{6} +^{48} C_{6} + \dots . +^{30} C_{6}$

$\begin{array}{r} =^{50} C_{6} +^{49} C_{6} +^{48} C_{6} + \dots . + (^{30} C_{6} +^{30} C_{7}) -^{30} C_{7} \\ =^{50} C_{6} +^{49} C_{6} +^{48} C_{6} + \dots . + (^{31} C_{6} +^{31} C_{7}) -^{30} C_{7} \\ =^{50} C_{6} +^{50} C_{7} -^{30} C_{7} \\ =^{51} C_{7} -^{30} C_{7} \end{array}$

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The angle of elevation of a cloud $C$ from a point $P, 200 m$ above a still take is $30^{\circ}$ . If the angle of depression of the image of $C$ in the lake from the point $P$ is $60^{\circ}$ , then $P C$ (in $m$ ) is equal to

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The angle of elevation of a cloud C from a point P,200m above a still take is 30∘ . If the angle of depression of the image of C in the lake from the point P is 60∘ , then PC (in m ) is equal to

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The angle of elevation of a cloud $C$ from a point $P, 200 m$ above a still take is $30^{\circ}$ . If the angle of depression of the image of $C$ in the lake from the point $P$ is $60^{\circ}$ , then $P C$ (in $m$ ) is equal to