Question

Instructions: Find the missing side lengths. Leave your answers as radicals in simplest form.

Answer 1

`a = 4`

`b = 2√(3)`

Explanation:

✔️Solving for a using trigonometric ratio:

reference angle = 60°

hypotenuse = a

adjacent = 2

Thus:

`cos(60) = (2)/(a)`

`(1)/(2) = (2)/(a)` (cos 60 = ½)

Cross multiply

`1*a = 2*2`

`a = 4`

✔️Solving for b using trigonometric ratio:

reference angle = 60°

Opposite = b

Adjacent = 2

Thus:

`tan(60) = (b)/(2)`

Multiply both sides by 2

`tan(60)*2 = (b)/(2)*2`

`tan(60)*2 = b`

`√(3)*2 = b` (tan 60 = √3)

`2√(3) = b`

`b = 2√(3)`