how do you find angle measures of an obtuse triangle when you know that the side lengths are 5, 9, and 11
+130466 The obtuse angle in any triangle will be opposite the longest side. We can use the Law of Cosines to find this. So we have
11^2 = 9^2 + 5^2 - 2(9)(5)cosx where x is the angle we're looking for
121 = 81 + 25 - 90cosx rearranging, we have
90cosx = 81 + 25 - 121 simplify on the right
90cosx = -15 divide both sides by 90
cosx = -15/90 = -1/6 use the acos function to find x
acos(-1/6) = x ≈ 99.59°
+130466 The obtuse angle in any triangle will be opposite the longest side. We can use the Law of Cosines to find this. So we have
11^2 = 9^2 + 5^2 - 2(9)(5)cosx where x is the angle we're looking for
121 = 81 + 25 - 90cosx rearranging, we have
90cosx = 81 + 25 - 121 simplify on the right
90cosx = -15 divide both sides by 90
cosx = -15/90 = -1/6 use the acos function to find x
acos(-1/6) = x ≈ 99.59°
