SOLUTION: If the sides of a triangle are AB=16, BC=16, and AC=23 what is each degree of all three angles

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Question 278179: If the sides of a triangle are AB=16, BC=16, and AC=23 what is each degree of all three angles
Answer by Edwin McCravy(20081) About Me  (Show Source):
You can put this solution on YOUR website!
If the sides of a triangle are AB=16, BC=16, and AC=23
what is each degree of all three angles.

Let a=BC, b=AC, c=AB



We use the law of cosines:

cos%28A%29=%28b%5E2%2Bc%5E2-a%5E2%29%2F%282bc%29

cos%28A%29=%2823%5E2%2B16%5E2-16%5E2%29%2F%282%2A23%2A16%29

cos%28A%29=529%2F736

cos%28A%29=.71875

A=%2244.04862567%B0%22 or A=%2244%B02%2755.052%27%27%22

--------------------------

cos%28B%29=%28a%5E2%2Bc%5E2-b%5E2%29%2F%282ac%29

cos%28B%29=%2816%5E2%2B16%5E2-23%5E2%29%2F%282%2A16%2A16%29

cos%28B%29=-17%2F512

cos%28B%29=-.033203125

B=%2291.90274865%B0%22 or B=%2291%B054%279.895%27%27%22
 
--------------------------

Since ABC is isosceles, we know that angle C=angle A,
or we can calculate it as a check with the law of cosines:

cos%28C%29=%28a%5E2%2Bb%5E2-c%5E2%29%2F%282ab%29

cos%28C%29=%2816%5E2%2B23%5E2-16%5E2%29%2F%282%2A16%2A23%29

cos%28C%29=529%2F736

cos%28C%29=.71875

C=%2244.04862567%B0%22 or A=%2244%B02%2755.052%27%27%22

Edwin