Law of Sines and Cosines

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: Sin(A)/a = Sin(B)/b = Sin(C)/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

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: c² = a² + b² - 2ab * cos(C).

Front

When do you 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) of a triangle.

Front

Calculate the distance from a point to a kite if the angle of elevation is 65 degrees and the string length is 75 feet.

Back

Distance = 75 * sin(65) = 96.36 feet.

Front

If two angles of a triangle are 55 degrees and 63 degrees, what is the third angle?

Back

The third angle is 180 - (55 + 63) = 62 degrees.

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 sides and C is the included angle.

Front

What is the sine of an angle in a right 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 right triangle?

Back

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

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).