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Applications of TrigonometryMathsClass 12thNcert Solutions Maths class 12th

A man is observing, from the top of a tower, a boat speeding towards the tower from a certain point A, with uniform speed. At that point, angle of depression of the boat with the man's eye is 30° (Ignore man's height). After sailing for 20 seconds, towards the base of the tower (which is the level of water), the boat has reached a point B, where the angel of depression is 45°. Then the time taken (in second) by the boat from B to reach the base of the tower is:

Option 1 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mn>1</mn> <mn>0</mn> <mrow> <mo>(</mo> <mrow> <mroot> <mrow> <mn>3</mn> </mrow> <mrow></mrow> </mroot> <mo>−</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> </math> </span></p>
Option 2 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mn>1</mn> <mn>0</mn> <mrow> <mo>(</mo> <mrow> <mroot> <mrow> <mn>3</mn> </mrow> <mrow></mrow> </mroot> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> </math> </span></p>
Option 3 - <p>10</p>
Option 4 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mn>1</mn> <mn>0</mn> <mroot> <mrow> <mn>3</mn> </mrow> <mrow></mrow> </mroot> </mrow> </math> </span></p>
3 Views|Posted 4 months ago
Asked by Shiksha User
1 Answer
V
4 months ago
Correct Option - 2
Detailed Solution:

∴ I n     Δ A Q P

t a n 3 0 ° = P Q A Q

1 3 = h x + y

x + y = 3 h . . . . . ( i )

∴ l n     Δ B Q P

t a n 4 5 ° = h y

h = y . (ii)

(i) & (ii) x + y = 3 y

⇒ x = ( 3 − 1 ) y . . . . . . . ( i i i )

Let the speed be S

x S = 2 0

x = 20.S

from (iii)

y S = 1 0 ( 3 + 1 )

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Let AB and PQ be two vertical poles, 160m apart from each other. Let C be the middle points of B and Q, which are feet of these two poles. Let π 8 <!-- [if gte mso 9]><xml> </xml><![endif]--> and q be the angles of elevation from C to P and A, respectively. If the height of pole PQ is twice the height of pole AB, then tan2q is equal to

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Payal Gupta
tanπ8=2h80......... (i)

tanθ=h80.......... (ii)

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tan2θ=3−224

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Maths Ncert Solutions class 12th 2026

Maths Ncert Solutions class 12th 2026

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