Answer:
θ = 36°
Explanation:
The Law of Cosines has three equations:
a^2 = b^2 + c^2 - 2bc * cos (A)
b^2 = a^2 + c^2 - 2ac * cos (B)
c^2 = a^2 + b^2 - 2ab * cos (C)
Let's call the 15 mm side c, the 23 mm side a and the 12 mm side b, and angle θ angle C . Thus, we can use the third equation and plug in 15 for c, 23 for a, and 12 for b to find the measure of angle C (i.e., the measure of θ to the nearest degree):
Step 1: Plug in 15, 23, and 12 and simplify:
c^2 = a^2 + b^2 - 2ab * cos (C)
15^2 = 23^2 + 12^2 -2(23)(12) * cos (C)
225 = 529 + 144 - 552 * cos (C)
225 = 673 - 552 * cos (C)
Step 2: Subtract 673 from both sides:
(225 = 673 - 552 * cos (C)) - 673
-448 = -552 * cos (C)
Step 3: Divide both sides by -552:
(-448 = -552 * cos (C)) / -552
-448/-552 = cos (C)
56/69 = cos (θ)
Step 4: Use inverse cosine to find C and round to the nearest degree (i.e., the nearest whole number):
cos^-1 (56/69) = C
35.74801694 = C
36 = C
36 = θ
Thus, angle θ is about 36°.