Problem solving

Question

What is the measure of the largest angle of a triangle having the sides 215, 309, 278?

Answer 1

The largest angle in a triangle is across from the triangle's largest side. So, using the law of cosines, we can find the measure of the angle across from the 309-length side:

 

c² = a² + b² - 2ab(cosC)

(309)² = (215)² + (278)² - 2(215)(278)(cosC)

95481 = 46225 + 77284 - (119540)(cosC)

95481 = 123509 - (119540)(cosC)

-28028 = -119540(cosC)

0.234465 = cosC

76.44 = C

 

So, the triangle's largest angle-measure is 76.44°.