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

Instructions: Find the missing side lengths. Leave your answers as radicals in simplest-example-1

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Answer:


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)

User Alfallouji
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