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  • Two sides and the angle

Area of a triangle with sine worksheets

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. These free printable worksheets give the two sides and the included angle and ask for the area, rounded to one decimal place.

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Ready to printArea of a triangle with sine
Area of a triangle with sine worksheet — Two sides and the angle, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

The formula is the familiar ½ base × height with the height replaced by b·sin C — because the height dropped from one vertex is the other side times the sine of the angle between them. So no perpendicular has to be found first, which is exactly when this rule earns its place.

Why this sheet works

It is a calculator worksheet and prints for that reason: sin C comes from a calculator and the area is rounded off. The answer is asked to one decimal place, the answer key gives the rounded value, and the step-by-step walk substitutes the two sides and the included angle into ½ab·sin C.

How this one works

One question from this sheet, worked through a step at a time.

Find the area

Area=½ · a · b · sin C
Area=½ · 7 · 7 · sin 80°
Area≈24.1
  1. Two sides and the angle between them give the area directly: Area = ½·a·b·sin C.
  2. Substitute a = 7, b = 7, C = 80°.
  3. Evaluate and round: Area ≈ 24.1.

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