Question

if alpha plus beta equals to 90 degree and alpha by beta equals to 2 by 1 find the value of sin alpha by sin beta​

Answer 1

Given:

$\alpha + \beta =90$  --------(1)

$\frac{\alpha}{\beta} = \frac{2}{1}$

⇒ $\alpha =2 \beta$

Putting the value of a in (1),

⇒ $2\beta+\beta=90$

⇒ $3\beta=90$

⇒ $\beta=30$

⇒ $\alpha=60$

⇒ $sin\alpha = sin 60$

⇒$sin\alpha =\frac{\sqrt{3} }{2}$

⇒$sin\beta = sin30$

⇒$sin\beta =\frac{1}{2}$

⇒$\frac{sin\alpha }{sin\beta } = \frac{\frac{\sqrt{3} }{2} }{\frac{1}{2} }$

⇒ $\frac{sin\alpha }{sin\beta } = \frac{\sqrt{3} }{1}$