Question

If α + β = 90° and α:β = 2:1 , then find the value of Sinα :Sinβ

Answer 1

Answer:

√3

Step-by-step explanation:

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Answer 2

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☞ Sin α : Sin β = √3 : 1

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➝ α + β = 90°

➝ α : β = 2 : 1

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✭ Value of Sin α : Sin β

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➳ α + β = 90

Let β = 2x and β = X .

Sum of a + b will be :-

➳ 2x + X = 3x.

$\begin{lgathered}\sf{\dashrightarrow a = \dfrac{2x}{3x} \times 90 }\end{lgathered}$

$\begin{lgathered}\sf{\dashrightarrow a = 2 \times 30 = 60 }\end{lgathered}$

➳ α + β = 90

➳ 60 + β = 90

➳ β = 30 °

Putting the values of Sin α and Sin β :

$\begin{lgathered}\sf\twoheadrightarrow \dfrac{ sin(\alpha) }{ sin(\beta) } = \dfrac{ sin(60) }{ sin(30) } \end{lgathered}$

$\begin{lgathered}\sf\twoheadrightarrow sin 60= \dfrac{ \sqrt{3} }{ 2 } \end{lgathered}$

$\begin{lgathered}\sf\twoheadrightarrow sin 30= \dfrac{ 1 }{ 2 } \end{lgathered}$

Putting these values in ratio :

$\begin{lgathered}\sf\leadsto \: \dfrac{ sin(\alpha) }{ \sin(\beta) } = \dfrac{ \dfrac{ \sqrt{3} }{2} }{ \dfrac{1}{2} } \end{lgathered}$

$\begin{lgathered}\sf\leadsto \: \dfrac{ sin(\alpha) }{ sin(\beta) } = \dfrac{ \sqrt{3} }{2} \times 2 \end{lgathered}$

$\sf\orange{\leadsto{\dfrac{sin(\alpha)}{sin(\beta)} = \dfrac{\sqrt{3}}{1}}}$

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