Question

If tan(90° - A) = √3, what is sin A?

• A. 1/2
• B. √3/2
• C. √2/2
• D. 3/4

Answer 1

Answer:

A. 1/2

Given:

$\tan(90^\circ - A) = \sqrt{3}$

Using identity:

$\tan(90^\circ - A) = \cot A$

So,

$\cot A = \sqrt{3}$
$\Rightarrow \tan A = \frac{1}{\sqrt{3}}$

We know:

$\tan A = \frac{\text{opposite}}{\text{adjacent}} = \frac{1}{\sqrt{3}}$

Take:

• Opposite = 1

• Adjacent = √3

Hypotenuse:

$\sqrt{1^2 + (\sqrt{3})^2} = \sqrt{1+3} = 2$

So,

$\sin A = \frac{1}{2}$