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 the angle opposite that side is constant for all three sides and angles in the triangle. Formula: 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. Formula: c² = a² + b² - 2ab*cos(C).

Front

When do you use the Law of Sines?

Back

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

Front

When do you use the Law of Cosines?

Back

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

Front

Calculate the length of side c in a triangle with sides a = 6 m, b = 8 m, and included angle C = 137°.

Back

c = 13.0 m.

Front

What is the formula for the Law of Cosines?

Back

c² = a² + b² - 2ab*cos(C).

Front

If a triangle has sides of lengths 7, 24, and 25, is it a right triangle?

Back

Yes, because 7² + 24² = 25² (49 + 576 = 625).

Front

Find the distance from Point A to Point B given Point C is 860 feet from A, 175 feet from B, and angle C = 78 degrees.

Back

Distance AB = 841.22 feet.

Front

What is the sine of an angle in a triangle?

Back

The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.

Front

What is the cosine of an angle in a triangle?

Back

The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.