Law of Sines & Cosines Practice

The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. It can be expressed as: a/sin(A) = b/sin(B) = c/sin(C).

The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. It is expressed as: c² = a² + b² - 2ab*cos(C).

To find a missing side using the Law of Sines, set up the ratio a/sin(A) = b/sin(B) and solve for the unknown side.

To find a missing side using the Law of Cosines, use the formula c² = a² + b² - 2ab*cos(C) and solve for the unknown side.

Identify the known sides and the included angle of the triangle.

Identify the known angles and the corresponding sides of the triangle.

Use the formula b = a * (sin(B)/sin(A)).

In a triangle, larger angles are opposite longer sides, and smaller angles are opposite shorter sides.

Rearrange the Law of Cosines formula to solve for the angle: C = cos⁻¹((a² + b² - c²) / (2ab)).

The Law of Sines allows for the calculation of unknown sides and angles in any triangle, not just right triangles.