Question

Suppose a triangle has sides a, b, c, and the angle opposite the side of length "a" is obtuse. What must be true?

Answer 1

a^2+b^2=c^2 is a right angled triangle. You're given that a^2+b^2>c^2 cos(A) = [a^2+b^2-c^2]/2ab c^2+2ab*cos(A) = a^2+b^2 Thus, c^2+2ab*cos(A) > c^2 cos(A)>0 A>90 degrees. ie Obtuse triangle. If a^2+b^2 < c^2. A<90 degrees ie. Acute triangle. Hypotenuse is c. Use the law of cosines.

Answer 2

angles corespond with legnth of side
angle oposite a is obtuse
osbtuse meas move than 90
all angles in a triangle add to 180
180/2=90
since that angle oposite a is bigger than half, that angle is bigger than the oterh angles
so therefor
a>b
a>c


we know that from pythagoran theorem that the square of the longest side is equal to the squares of the other 2 sides
the angle oposite that longest side is 90
obtuse>90 so it is longer legnth
a is longest side
b^2+c^2<a^2

the answer is D