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

Question

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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Autumn 3 weeks 2021-11-08T12:15:33+00:00 1 Answer 0 views 0

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    2021-11-08T12:17:21+00:00

    Answer:

    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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45:7+7-4:2-5:5*4+35:2 =? ( )