# If cosA=3/10 what is tanA?

Dec 14, 2016

$\tan A = \frac{\sqrt{91}}{3}$
Since the cosine ratio is the adjacent over the hypotenuse, we can use the Pythagorean Theorem to solve for the third side (opposite leg). ${3}^{2} + {y}^{2} = {10}^{2}$
So, ${y}^{2} = 100 - 9$ or ${y}^{2} = 91$
then, $y = \sqrt{91}$.
Tangent of angle A will be: $\frac{\sqrt{91}}{3}$