Question

Law of cosines in (triangle )rst if r = 14 yd s = 9 yd t = 6 yd find m

Answer 1

In a triangle ABC, the law of cosines can be illustrated using the rules found in the attached image.

Now, applying this rule to the given triangle, we can calculate the measure of each angle as follows:
cos(r) = (s^2 + t^2 - r^2) / (2st) = (9^2 + 6^2 - 14^2) / (2*9*6) = -0.73148
angle r = 137.01 which is approximately 137 degrees

cos(s) = (r^2 + t^2 - s^2) / (2rt) = (14^2 + 6^2 - 9^2) / (2*14*6) = 0.8988
angle s = 25.99797 which is approximately 26 degrees

cos(t) = (r^2 + s^2 - t^2) / (2rs) = (14^2 + 9^2 - 6^2) / (2*14*9) = 0.9563
angle t = 16.99 which is approximately 17 degrees

Summing up the calculated angles:
sum = 137 + 26 + 17 = 180 degrees
which is the sum of the angles of the triangle