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30 June, 15:48

In right triangle JFK sin (52) = cos (5x-2). What is the measure of the smallest angle in the triangle?

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  1. 30 June, 16:15
    0
    48°

    Step-by-step explanation:

    Given the trigonometry equation

    sin (52) = cos (5x-2) ... 1

    According to the quadrant:

    Sin (θ) = cos (90-θ)

    Sin52 = cos (90-52)

    Sin52 = cos48 ... 2

    Substituting 2 into 1:

    Cos48 = cos (5x-2)

    48 = 5x-2

    5x = 48+2

    5x = 50

    x = 10°

    The smallest of the angle will be angle 5x-2 = 5 (10) - 2

    = 50-2

    = 48°
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