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A man observes that when he moves up a distance c metres on

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A man observes that when he moves up a distance $c$ metres on a slope, the angle of depression of a point on the horizontal plane from the base of the slope is $30^{o}$ and when he moves up further a distance $c$ metres, the angle of depression of that point is $45^{o}$ . The angle of inclination of the slope with the horizontal is

60^{o}

45^{o}

75^{o}

30^{o}

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A man observes that when he moves up a distance

c

metres on a slope, the angle of depression of a point on the horizontal plane from the base of the slope is

30^{o}

and when he moves up further a distance

c

metres, the angle of depression of that point is

45^{o}

. The angle of inclination of the slope with the horizontal is

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Text solutionVerified

Applying m-n theorem of trigonometry, we get

(c + c) cot (θ - 30) = c cot 15 - c cot 30

\Rightarrow cot (θ - 30) = \frac{1}{2} \frac{sin ( 30 - 15 )}{sin 15 sin 30}

\Rightarrow cot (θ - 30) = \frac{1}{2} \frac{1}{sin 30}

\Rightarrow cot (θ - 30) = 1

\Rightarrow cot (θ - 30) = cot 45

\Rightarrow θ - 30 = 45

∴ θ = 7 5^{o}

So, angle of inclination if the slope with horizontal will be

7 5^{o}

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Question Text	A man observes that when he moves up a distance $c$ metres on a slope, the angle of depression of a point on the horizontal plane from the base of the slope is $30^{o}$ and when he moves up further a distance $c$ metres, the angle of depression of that point is $45^{o}$ . The angle of inclination of the slope with the horizontal is
Answer Type	Text solution:1
Upvotes	150