Area of a triangle with sine, step by step
When the height is unknown but two sides and the angle between them are given, the area of a triangle is ½·a·b·sin C.
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°.
- Evaluate and round: Area ≈ 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
Evaluate and round: Area ≈ 24.7.