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.

Question

24 degrees
24 degrees

19 degrees
19 degrees

28 degrees
28 degrees

133 degrees

Answer 1

To find the measure of ∠C, we can use the Law of Cosines. The formula is as follows:

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

Plugging in the given values:

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

Simplifying:

400 = 2116 + 900 - 2760 * cos(C)

Combining like terms:

0 = 4016 - 2760 * cos(C)

Rearranging:

2760 * cos(C) = 4016

cos(C) = 4016 / 2760

Taking the inverse cosine of both sides:

C = cos^(-1)(4016/2760)

Using a calculator, we find:

C ≈ 24 degrees

Therefore, the measure of ∠C is approximately 24 degrees. Answer: 24 degrees