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

    b = adjacent 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

    adjacent leg = 7√3 in

    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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