The area of a triangle ABC is 5cm2
AB=2cm and BC=5cm.
How much is AC?
No calculators, please..
(In reply to Solution
by Kenny M)
While perhaps trivial, this occurred to me: given a and b and Area and then asked to find c would have yielded two answers, had not Area = 1/2 a b. That the area is maximized with a right angle, and so gives a single answer, is proven by differentiation:
Area = 1/2 a b sin_theta
d_Area/d_sin_theta = 0
gives theta = 90.
For smaller Areas, the two sin_theta solutions are the acute and obtuse angles on either side of 90, and had Area been greater than 1/2 a b, there'd be no answer at all.
Edited on March 6, 2021, 6:27 pm