Problem 171
a. If you begin with a right triangle with sides a, b, and
c and decrease the right angle so it is an acute angle,
how does a2 + b2 compare with c2?
b. Answer this question for the situation where you
increase the right angle so that it is obtuse.
Solution
a. From the law of cosines, we know that c2 = a2 + b2 – 2abcos(α).
When α = 90, i.e. we have a right triangle, c2 = a2 + b2.
When we make α < 90 (acute), 2abcos(α) > 0, and
c2 < a2 + b2
b. When we make α > 90 (obtuse), 2abcos(α) < 0, and
c2 < a2 + b2