A triangle has side lengths of 9 in, 13 in, and 20 in. What is the measurement of this triangle's largest angle?

Accepted Solution

1. Given any triangle ABC with sides BC=a, AC=b and AB=c, the following are true :      i) the larger the angle, the larger the side in front of it, and the other way around as well. (Sine Law) Let a=20 in, then the largest angle is angle A.       ii) Given the measures of the sides of a triangle. Then the cosines of any of the angles can be found by the following formula:        a^{2}=b ^{2}+c ^{2}-2bc(cosA)2. 20^{2}=9 ^{2}+13 ^{2}-2*9*13(cosA)

400=81+169-234(cosA)   150=-234(cosA)

cosA=150/-234= -0.6413. m(A) = Arccos(-0.641)≈130°, 4. Remark: We calculate Arccos with a scientific calculator or computer software unless it is one of the well known values, ex Arccos(0.5)=60°, Arccos(-0.5)=120° etc