# Algebra

In a right triangle the leg opposite to the acute angle of 30° is 7 in. Find the hypotenuse and other leg.

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1. a = opposite leg

c = hypotenuse

tan θ = opposite leg / adjacent leg

tan θ = a / b

sin θ = opposite leg / hypotenuse

sin θ = a / c

θ = 30° , sin θ = 1 / 2 , tan θ = √3 / 3 , a = 7 in

tan θ = a / b

√3 / 3 = 7 / b

Multiply both sides by 3

√3 = 21 / b

Multiply both sides by b

√3 b = 21

Divide both sides by √3

b = 21 / √3 = 7 ∙ 3 / √3 = 7 ∙ √3 ∙ √3 / √3 = 7√3

sin θ = a / c

1 / 2 = 7 / c

Multiply both sides by 2

1 = 14 / c

Multiply both sides by c

c = 14

hypotenuse = 14 in

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2. Tan30 = Y/X = 7/X.
X = 7/Tan30 = 12.

sin30 = Y/r = 7/r.
r = 7/sin30 = 14. = hyp.

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