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23 May, 18:14

A right triangle has side lengths that are consecutive integers and a perimeter of 12 feet. What are

the angles of the triangle?

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Answers (1)
  1. 23 May, 22:05
    0
    The measures of the angles are 36.9 deg, 53.1 deg, 90 deg.

    Step-by-step explanation:

    The lengths of the sides are the famous Pythagorean triple: 3, 4, 5.

    To find the angles, we use trigonometry.

    Since it's a right angle, the longest side is the hypotenuse.

    The hypotenuse has length 5.

    The legs have lengths 3 and 4.

    tan A = opp/adj

    A = tan^ (-1) opp/adj

    A = tan^ (-1) 4/3 = 53.1 deg

    The acute angles of a right triangle are complementary.

    B = 90 - A = 90 deg - 53.1 deg = 36.9 deg

    Answer:

    The measures of the angles are 36.9 deg, 53.1 deg, 90 deg.
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