Question

Identify the values of the variables. Give your answers in the simplest radical form.

Answer 1

Answer/Step-by-step explanation:

✔️Find k:

Reference angle = 60°

Hypotenuse = k

Opposite = 9

Therefore, using trigonometric ratio, we have:

$sin(60) = \frac{9}{k}$

Multiply both sides by k

$k*sin(60) = 9$

Divide both sides by sin(60)

$k = \frac{9}{sin(60)}$

$k = \frac{9}{\frac{\sqrt{3}}{2}}$

$k = 9*\frac{2}{\sqrt{3}}$

$k = \frac{18}{\sqrt{3}}$

Rationalize

$k = \frac{18*\sqrt{3}}{\sqrt{3}*\sqrt{3}}$

$k = \frac{18\sqrt{3}}{3}$

$k = 6\sqrt{3}$

✔️Find f:

Reference angle = 60°

Opposite = 9

Adjacent = f

Therefore, using trigonometric ratio, we have:

$tan(60) = \frac{9}{f}$

Multiply both sides by f

$f*tan(60) = 9$

Divide both sides by tan(60)

$f = \frac{9}{tan(60)}$

$k = \frac{9}{\sqrt{3}}$

Rationalize

$k = \frac{9*\sqrt{3}}{\sqrt{3}*\sqrt{3}}$

$k = \frac{9\sqrt{3}}{3}$

$k = 3\sqrt{3}$