Given: △abc, m∠a=60°, m∠c=45°, ab=9 find: perimeter of △abc, area of △abc do not rationlize

p = 32.32; A = 47.91  

Step-by-step explanation:

1. Calculate ∠B

∠A + ∠B + ∠C = 180°

60° + ∠B + 45° = 180°

       ∠B + 105° = 180°

                  ∠B =   75°

2. Find sides BC and AC

We can use the Law of Sines

(i) Find BC

(ii) Find AC

3. Find the perimeter

p = AB + AC + BC = 9 + 12.29 + 11.02 = 32.32

4. Find the area of the triangle

A general formula for the area of a triangle is

A = ½ab sinC

If we use ∠A, the formula becomes

A = ½ × 9 × 12.29 × sin60° = 55.30 × 0.8660 = 47.91

by definition, an arc subtended by a central angle of some given measure has the same measure. so .