Given: △ABC, m∠A=60°, m∠C=45°, AB=9 Find: Perimeter of △ABC, Area of △ABC do not rationlize
1 answer:
Answer:
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
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