Question

Given sin A=-5/and that angle Ais in Quadrant III, find the exact value oftan Ain simplest radical form using a rational denominator.

Answer 1

Given:

$\sin A=-\frac{5}{\sqrt[]{61}}$

the angle A is in QIII, So, the value of the tan A will be positive

To find tan A, we need to find the third side of the right-angle triangle that angle A fall inside it

From the sin A = opposite/hypotenuse

opposite side = 5

hypotenuse = √61

the adjacent side will be calculated using the Pythagorean theorem

$adjacent=\sqrt[]{(\sqrt[]{61})^2-5^2}=\sqrt[]{61-25}=\sqrt[]{36}=6$

The value of tan A will be as follows:

$\begin{gathered} \tan A=\frac{opposite}{adjacent} \\ \\ \tan A=\frac{5}{6} \end{gathered}$