Question

Given, A and B are complementary angles, and sinA = 3, what is tanB?

• A. 4/3
• B. 3/4
• C. 5/4
• D. 5/3

Answer 1

Answer:

A. 4/3

Since A and B are complementary angles:

$B = 90^\circ - A$

And,

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

The question likely intends:

$\sin A = \frac{3}{5}$

because $(\sin A = 3)$ is not possible for an angle.

Using $(\sin A = \frac{3}{5}):$

$\cos A = \frac{4}{5}$

So,

$\cot A = \frac{\cos A}{\sin A}$
$= \frac{4/5}{3/5}$
$= \frac{4}{3}$

Therefore,

$\tan B = \frac{4}{3}$

So the answer is:

$\boxed{\frac{4}{3}}$