Law of Sines & Cosines Practice

Front

What is the Law of Sines?

Back

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).

Front

What is the Law of Cosines?

Back

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).

Front

How do you use the Law of Sines to find a missing side?

Back

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.

Front

How do you use the Law of Cosines to find a missing side?

Back

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.

Front

What is the first step in applying the Law of Cosines?

Back

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

Front

What is the first step in applying the Law of Sines?

Back

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

Front

If angle A = 50 degrees and side a = 10, how do you find side b using the Law of Sines?

Back

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

Front

What is the relationship between the angles and sides in a triangle?

Back

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

Front

How can the Law of Cosines be used to find an angle?

Back

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

Front

What is the significance of the Law of Sines in non-right triangles?

Back

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