Law of Sines & Cosines Practice

Front

What is the Law of Sines?

Back

The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant for all three sides of the triangle. It is 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 used to find a side when two sides and the included angle are known, and is expressed as: c² = a² + b² - 2ab*cos(C).

Front

When do you 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) in a triangle.

Front

When do you use the Law of Cosines?

Back

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

Front

Calculate the length of side x if the triangle has sides 7 cm, 10 cm, and an angle of 45 degrees opposite side x.

Back

x = 7 * sin(45°) / sin(A) where A is the angle opposite the 7 cm side.

Front

If angle A = 30°, angle B = 60°, and side a = 10 cm, what is side b using the Law of Sines?

Back

b = (10 * sin(60°)) / sin(30°) = 17.32 cm.

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

If a triangle has sides of lengths 8 cm, 15 cm, and an angle of 60° between them, find the length of the third side using the Law of Cosines.

Back

c² = 8² + 15² - 2*8*15*cos(60°) => c = √(64 + 225 - 120) = √169 = 13 cm.

Front

What is the relationship between the angles and sides in a triangle according to the Law of Sines?

Back

The Law of Sines shows that larger angles are opposite longer sides, and smaller angles are opposite shorter sides.

Front

How do you find the angle of a triangle if you know all three sides?

Back

Use the Law of Cosines: cos(C) = (a² + b² - c²) / (2ab) to find angle C, then use the Law of Sines to find the other angles.