SOLUTION: Help! Consider a triangle with side lengths a=3, b=4. and c=6. Can it be a right triangle? What are the measures, to the nearest degree, of the three angles?

Algebra ->  Trigonometry-basics -> SOLUTION: Help! Consider a triangle with side lengths a=3, b=4. and c=6. Can it be a right triangle? What are the measures, to the nearest degree, of the three angles?       Log On


   

Question 1005028: Help!
Consider a triangle with side lengths a=3, b=4. and c=6. Can it be a right triangle? What are the measures, to the nearest degree, of the three angles?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Use the longest side as a hypotenuse to test in the Pythagorean Theorem formula. Does the formula give a true statement or a false statement?


You will want to use Law Of Cosines to find the three angle measures.
highlight_green%28a%5E2%2Bb%5E2-2ab%2Acos%28gamma%29=c%5E2%29, which you apply appropriately for all three angles of your triangle.

-2ab%2Acos%28gamma%29=c%5E2-a%5E2-b%5E2

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

cos%28gamma%29=%289%2B16-36%29%2F%282%2A12%29

cos%28gamma%29=-11%2F24
gamma=117.28%2Adegrees