In triangle ABC, a = 12, b = 10, and c = 9 . Find the measure of the largest angle in triangle ABC.
the law of sines says that the angle opposite side a will be the largest.
Use the law of cosines to find that angle.
To find the measure of the largest angle in triangle ABC, we can use the Law of Cosines. The Law of Cosines states that for any triangle with side lengths a, b, and c, and opposite angles A, B, and C respectively, the following equation holds:
c^2 = a^2 + b^2 - 2ab * cos(C)
In this case, we are given the side lengths a = 12, b = 10, and c = 9. We want to find the largest angle, which in this case is angle C.
Let's substitute the given values into the equation:
9^2 = 12^2 + 10^2 - 2 * 12 * 10 * cos(C)
81 = 144 + 100 - 240 * cos(C)
To solve for cos(C), we can rearrange the equation as follows:
240 * cos(C) = 144 + 100 - 81
240 * cos(C) = 163
cos(C) = 163 / 240
Now, we can find the value of cos(C) using a calculator:
cos(C) ≈ 0.6792
To find angle C, we can take the inverse cosine (or arc cosine) of cos(C):
C ≈ cos^(-1)(0.6792)
Using a calculator, we get:
C ≈ 46.86 degrees
Therefore, the measure of the largest angle in triangle ABC is approximately 46.86 degrees.