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°
Area24.7
  1. Two sides and the angle between them give the area directly: Area = ½·a·b·sin C.
  2. Substitute a = 7, b = 11, C = 40°.
  3. Evaluate and round: Area ≈ 24.7.

How it works.

  1. 01

    Two sides and the angle between them give the area directly: Area = ½·a·b·sin C.

  2. 02

    Substitute a = 7, b = 11, C = 40°.

  3. 03

    Evaluate and round: Area ≈ 24.7.