A triangle has two corners of angles #pi /6# and #(5pi)/8 #. What are the complement and supplement of the third corner?

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Answer 1 · 2017-01-19T05:51:10

The complement would be #(7pi)/24# and the supplement #(19pi)/24#

A triangle always has #180^@# worth of angle. That is #pi# radians. #pi/6+(5pi)/8=(38pi)/48 => pi-(38pi)/48=(10pi)/48=(5pi)/24#

The complement #c# of the remaining corner would satisfy #(10pi)/48+c=pi/2=(24pi)/48 <=> c=(24pi)/48-(10pi)/48=(14pi)/48=(7pi)/24#

And the supplement #s# would be

#s=pi-(10pi)/48=(38pi)/48=(19pi)/24#