Given: ΔABC, AB = 7, BC= 8, AC = 9 Find: m∠A, m∠B, m∠C

Question

Given: ΔABC, AB = 7, BC= 8, AC = 9 Find: m∠A, m∠B, m∠C

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Eden 1 week 2021-10-07T12:48:41+00:00 1 Answer 0

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    2021-10-07T12:50:00+00:00

    Answer:

    Part 1) m\angle A=58.41^o

    Part 2) m\angle B=73.40^o

    Part 3) m\angle C=48.19^o

    Step-by-step explanation:

    step 1

    Find the measure of angle A

    we know that

    Applying the law of cosines

    BC^2=AB^2+AC^2-2(AB)(AC)cos(A)

    substitute the given values

    8^2=7^2+9^2-2(7)(9)cos(A)

    64=130-126cos(A)

    126cos(A)=130-64

    126cos(A)=66

    cos(A)=66/126

    using calculator

    m\angle A=cos^{-1}(66/126)= 58.41^o

    step 2

    Find the measure of angle B

    we know that

    Applying the law of cosines

    AC^2=AB^2+BC^2-2(AB)(BC)cos(B)

    substitute the given values

    9^2=7^2+8^2-2(7)(8)cos(B)

    81=113-112cos(B)

    112cos(B)=113-81

    112cos(B)=32

    cos(B)=32/112

    using calculator

    m\angle B=cos^{-1}(32/112)= 73.40^o

    step 3

    Find the measure of angle C

    Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

    so

    A+B+C=180^o

    substitute the given values

    58.41^o+73.40^o+C=180^o

    131.81^o+C=180^o

    C=180^o-131.81^o=48.19^o

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