Points A, B, and C are on the circumference of a circle with radius 2 such that angle BAC = 45 degrees and angle ACB = 60 degrees. Find the area of triangle ABC.

Answer 1

In triangle ABC, the angles are
A=45
C=60
so, B=75

These are inscribed angles, so if you draw radii from the center O to each vertex, you have

AOB = 2*ACB = 120
BOC = 2*BAC = 90
AOC = 2*ABC = 150

Now you have three isosceles triangles. Each triangle with central angle θ has area

a = 1/4 r^2 sinθ

Now just plug and chug. If you really want punishment, use the sum-to product formulas to reduce the answer to a single product.