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) = (9)/(k)`

Multiply both sides by k

`k*sin(60) = 9`

Divide both sides by sin(60)

`k = (9)/(sin(60))`

`k = (9)/((√(3))/(2))`

`k = 9*(2)/(√(3))`

`k = (18)/(√(3))`

Rationalize

`k = (18*√(3))/(√(3)*√(3))`

`k = (18√(3))/(3)`

`k = 6√(3)`

✔️Find f:

Reference angle = 60°

Opposite = 9

Adjacent = f

Therefore, using trigonometric ratio, we have:

`tan(60) = (9)/(f)`

Multiply both sides by f

`f*tan(60) = 9`

Divide both sides by tan(60)

`f = (9)/(tan(60))`

`k = (9)/(√(3))`

Rationalize

`k = (9*√(3))/(√(3)*√(3))`

`k = (9√(3))/(3)`

`k = 3√(3)`