Find the areas of triangles with the given parts:

Question

b =12, c =9, m∠A=57

A≈  sq. units

Answer 1

The base, b, of ABC is 12.

If you drop a line from point B to a point D on AC to form a right triangle, then AD = the height, h, of ABC.

Triangle ABD is a right triangle with the hypotenuse = 9.

AD = 9sin(57°) = 7.548

Area = (1/2)bh = (12/2)7.548 = 45.288 sq. units.

OR we could have just used the triangle area sine equation, Area = (1/2)cbsin(A)

Area = (9•12/2)sine(57°) ≈ 45.288 sq. units.