If two towers of height h1 and h2 substends angles of 60 - and 30 - mid point of the line joining their feet- Then what is h1-h2

REF.Image tan 30^∘=h_2/x #160; #160; tan 60^∘=h_1/x tan 60^∘/tan 30^∘=h_1/x/h_2/x=h_1/h_2 h_1/h_2=√(3)/1/√(3)=3/1 ...

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Standard X

Mathematics

Calculating Heights and Distances

If two towers...

Question

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 $h_{1} : h_{2}$

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Solution

REF.Image
$t a n 30^{\circ} = \frac{h_{2}}{x}$ $t a n 60^{\circ} = \frac{h_{1}}{x}$
$\frac{t a n 60^{\circ}}{t a n 30^{\circ}} = \frac{h_{1} / x}{h_{2} / x} = \frac{h_{1}}{h_{2}}$
$\frac{h_{1}}{h_{2}} = \frac{\sqrt{3}}{\frac{1}{\sqrt{3}}} = \frac{3}{1}$

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Similar questions

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.

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. 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} =

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

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 substends angles of 60∘ and 30∘ mid point of the line joining their feet. Then what is h1:h2

REF.Imagetan30∘=h2x tan60∘=h1xtan60∘tan30∘=h1/xh2/x=h1h2h1h2=√31√3=31

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 $h_{1} : h_{2}$

REF.Image
$t a n 30^{\circ} = \frac{h_{2}}{x}$ $t a n 60^{\circ} = \frac{h_{1}}{x}$
$\frac{t a n 60^{\circ}}{t a n 30^{\circ}} = \frac{h_{1} / x}{h_{2} / x} = \frac{h_{1}}{h_{2}}$
$\frac{h_{1}}{h_{2}} = \frac{\sqrt{3}}{\frac{1}{\sqrt{3}}} = \frac{3}{1}$