General triangle relationships

Choose sine, cosine, or area formulas appropriate to the triangle's given conditions.

Meaning

The sine and cosine rules connect sides and angles even without a right angle. The cosine rule becomes the Pythagorean theorem when the included angle is right.

Example

For sides 4 and 7 with included angle 60 degrees, the opposite side satisfies so it is Place the side of length 7 horizontally. The other side has horizontal component 4cos60° and height 4sin60°. The opposite side squared is (7−4cos60°)²+(4sin60°)²; using sin²+cos²=1 simplifies this to the cosine-rule expression.Match angles with their opposite sides. Two sides and a nonincluded angle can allow two triangles.

Practice for this concept

Scope and references

Topics

The sine rule, cosine rule, triangle area formulas

Learning goal

Choose sine, cosine, or area formulas appropriate to the triangle's given conditions.

Helpful background

Explore triangle sides, angles, and trigonometric ratios.