Question

if tan theta=√3 and (0°<theta<90°) find the value of sin theta​

Answer 1

Answer:

Tan theta= root 3

So theta = 60°

Therefore, sin theta= root3/2

[As theta = 60°]

Answer 2

Answer:

$\tan(x) = \sqrt{3} \\ \sin(x) = \cos(x) \tan(x) \\ \sin(x) = \cos(x) \sqrt{3} \\ \sin(x) = \sin(90 - x) \sqrt{3} \\ \frac{ \sin(x) }{ \sin(90 - x) } = \sqrt{3 } \\ \sqrt{3 } = \frac{x}{90 - x} \\ 90 \sqrt{3} - \sqrt{3} x = x \\ 90 \sqrt{3} = x + \sqrt{3} x \\ 90 \sqrt{3} = x(1 + \sqrt{3} ) \\ \frac{90 \sqrt{3} }{1 + \sqrt{3} } = x \\ x = \frac{90 \sqrt{3} }{ \sqrt{3}( \sqrt{3} + 1) } \\ x = \frac{90}{ \sqrt{3} + 1} \\ \sqrt{3} x + x = 90$

hope it helps