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 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

tanπ8=2h80......... (i) tanθ=h80.......... (ii) ⇒tanπ8=2tanθ tan2θ=3−224

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 $\frac{π}{8}$ 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

Option 1 - <math> <mrow> <mfrac> <mrow> <mn>3</mn> <mo>−</mo> <mn>2</mn> <mroot> <mrow> <mn>2</mn> </mrow> <mrow></mrow> </mroot> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </math>

Option 2 - <math> <mrow> <mfrac> <mrow> <mn>3</mn> <mo>+</mo> <mroot> <mrow> <mn>2</mn> </mrow> <mrow></mrow> </mroot> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </math>

Option 3 - <math> <mrow> <mfrac> <mrow> <mn>3</mn> <mo>−</mo> <mn>2</mn> <mroot> <mrow> <mn>2</mn> </mrow> <mrow></mrow> </mroot> </mrow> <mrow> <mn>4</mn> </mrow> </mfrac> </mrow> </math>

Option 4 - <math> <mrow> <mfrac> <mrow> <mn>3</mn> <mo>−</mo> <mroot> <mrow> <mn>2</mn> </mrow> <mrow></mrow> </mroot> </mrow> <mrow> <mn>4</mn> </mrow> </mfrac> </mrow> </math>

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Payal Gupta | Contributor-Level 10

6 months ago

Correct Option - 3

Detailed Solution:

t a n \frac{π}{8} = \frac{2 h}{80} . . . . . . . . . (i)

$t a n θ = \frac{h}{80} . . . . . . . . . . (i i)$

$\Rightarrow t a n \frac{π}{8} = 2 t a n θ$

$t a n^{2} θ = \frac{3 - 2 \sqrt[]{2}}{4}$

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