Question

Given a triangle with side lengths: root3, root3, 3, find the measure of its smallest angle.

Answer 1

well,
tan(x/2) = 2/√3

now just take 2*arctan(2/√3)

Answer 2

Since it is isosceles, we can construct a right-angled triangle with an altitude to the base of 3

then cosØ = 1.5/√3 = 3/2√3
= 3/2√3 * √3/√3
= √3 /2
ahhh, do you recognize the 30-60-90° triangle
(if not, use your calculator)

Ø = 30°

or

Answer 3

Dang. I used x as the vertex angle. Go with Reiny.