Area of a triangle with sine
The question
In △ABC, a = 7, b = 11, ∠C = 40°. Find the area:
Find the area
Area=½ · a · b · sin C
Area=½ · 7 · 11 · sin 40°
Area≈24.7
- Two sides and the angle between them give the area directly: Area = ½·a·b·sin C.
- Substitute a = 7, b = 11, C = 40°.
- ½ · 7 · 11 = 38.5, and sin 40° ≈ 0.6428, so Area ≈ 38.5 × 0.6428 ≈ 24.7.
How it works.
- 01
Two sides and the angle between them give the area directly: Area = ½·a·b·sin C.
- 02
Substitute a = 7, b = 11, C = 40°.
- 03
½ · 7 · 11 = 38.5, and sin 40° ≈ 0.6428, so Area ≈ 38.5 × 0.6428 ≈ 24.7.