Question

For ΔABC , find the measure of ∠C to the nearest degree when side a=46 m, side b=30 m, and side c=20 m. (1 point) Responses 133 degrees 133 degrees 19 degrees 19 degrees 28 degrees 28 degrees 24 degrees

Answer 1

To find the measure of angle C, we can use the Law of Cosines. The formula is given by:

c^2 = a^2 + b^2 - 2ab cos(C)

Substituting the given values, we have:

20^2 = 46^2 + 30^2 - 2(46)(30)cos(C)

400 = 2116 + 900 - 2760cos(C)

400 = 3116 - 2760cos(C)

2760cos(C) = 3116 - 400

2760cos(C) = 2716

cos(C) = 2716/2760

cos(C) = 0.986957

To find the measure of angle C, we can use the inverse cosine function:

C = cos^(-1)(0.986957)

C ≈ 20.869 degrees (rounded to the nearest degree)

Therefore, the measure of angle C is approximately 21 degrees.