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Standard IX

Mathematics

Trigonometric Ratios

If two towers...

Question

If two towers of height $h_{1} a n d h_{2}$ subtend angles $45^{\circ} a n d 30^{\circ}$ respectively at the midpoint of the line joining their feet, then find the ratio of

$h_{1} : h_{2} .$

$1 : 2$

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$3 : 2$

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$\sqrt{3} : 1$

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$1 : \sqrt{3}$

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Solution

The correct option is C
$\sqrt{3} : 1$

$t a n 45^{\circ} = \frac{h_{1}}{x} . . . . (1) t a n 30^{\circ} = \frac{h_{2}}{x} . . . . (2) \Rightarrow \frac{t a n 45^{\circ}}{t a n 30^{\circ}} = \frac{\frac{h_{1}}{x}}{\frac{h_{2}}{x}} h_{1} : h_{2} = \sqrt{3} : 1$

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Similar questions

If two towers of height $h_{1} a n d h_{2}$ subtend angles $45^{\circ} a n d 30^{\circ}$ respectively at the midpoint of the line joining their feet, then find the ratio of

$h_{1} : h_{2} .$

Q. If two towers of height h₁ and h₂ subtend angles of 60° and 30° respectively at the midpoint of the line joining their feet, then show that h₁ : h₂ = 3 : 1.

Q. Two towers of heights

h_{1}

and

h_{2}

subtend angles

60^{0}

and

30^{0}

respectively at the midpoint of the line joining their feet.

h_{1} : h_{2} =

Q. If two towers of height

h_{1}

and

h_{2}

substends angles of

60^{\circ}

and

30^{\circ}

mid point of the line joining their feet. Then what is

h_{1} : h_{2}

Q. Assertion (A)
If two towers of height h₁ and h₂ subtend angles of 60° and 30° respectively at the midpoint of the line joining their feet, then h₁ : h₂ = 3 : 1.

Reason (R)
Figure
In the given figure, we have:

\frac{h_{1}}{x} = \tan 60 ° and \frac{h_{2}}{x} = \tan 30 °

(a) Both Assertion (A) and Reason (R) are true and (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

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If two towers of height h1 and h2 subtend angles 45∘ and 30∘ respectively at the midpoint of the line joining their feet, then find the ratio of h1:h2.

The correct option is C √3:1 tan 45∘=h1x....(1)tan 30∘=h2x....(2)⇒tan 45∘tan 30∘=h1xh2xh1:h2=√3:1

If two towers of height $h_{1} a n d h_{2}$ subtend angles $45^{\circ} a n d 30^{\circ}$ respectively at the midpoint of the line joining their feet, then find the ratio of

$h_{1} : h_{2} .$

The correct option is C
$\sqrt{3} : 1$

$t a n 45^{\circ} = \frac{h_{1}}{x} . . . . (1) t a n 30^{\circ} = \frac{h_{2}}{x} . . . . (2) \Rightarrow \frac{t a n 45^{\circ}}{t a n 30^{\circ}} = \frac{\frac{h_{1}}{x}}{\frac{h_{2}}{x}} h_{1} : h_{2} = \sqrt{3} : 1$