Answer
38.83 cm, 67.61 degrees
Work Step by Step
Set up: Let the sides of the triangle be A, B, and C, where AB=AC. Draw an altitude (the height) from A to BC and let D be the point where the altitude intersects BC.
Finding the height: Triangles ABD and ACD are congruent, since triangle ABC is isosceles, so BD=CD=32/2=16. Then, using the Pythagorean Theorem, the height = AD = $\sqrt{42^2-16^2}=38.83$ centimeters.
Finding the angle: $cos$(angle ABD) = BD/AB = 16/42. So $cos^{-1}(16/42)=$angle ABD. Using a calculator, this gives 67.61 degrees.
