Law of Sines and Law of 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

How do you use the Law of Sines to find an unknown side?

Back

To find an unknown side using the Law of Sines, rearrange the formula to solve for the side: a = b * (sin(A) / sin(B)).

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 Cosines to find an unknown angle?

Back

To find an unknown angle using the Law of Cosines, rearrange the formula: C = cos⁻¹((a² + b² - c²) / (2ab)).

Front

What is the formula for finding the area of a triangle using the Law of Sines?

Back

Area = (1/2) * a * b * sin(C), where a and b are two sides and C is the included angle.

Front

When is it appropriate to use the Law of Sines?

Back

The Law of Sines is used when you have either two angles and one side (AAS or ASA) or two sides and a non-included angle (SSA).

Front

When is it appropriate to use the Law of Cosines?

Back

The Law of Cosines is used when you have either two sides and the included angle (SAS) or all three sides (SSS).

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 do you round numbers to the nearest tenth?

Back

To round to the nearest tenth, look at the hundredths place. If it's 5 or more, round up; if it's less than 5, round down.

Front

Solve for x using the Law of Sines: A = 30°, a = 10, B = 45°. What is x?

Back

x = 10 * (sin(45°) / sin(30°)) ≈ 14.1.