Law of Sines & Cosine

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 an unknown angle?

Back

To find an unknown angle using the Law of Sines, rearrange the formula: sin(A)/a = sin(B)/b. Solve for the angle using the inverse sine function: A = sin^(-1)(b*sin(B)/a).

Front

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

Back

To find an unknown side using the Law of Cosines, rearrange the formula: c = √(a² + b² - 2ab*cos(C)).

Front

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

Back

In a triangle, the larger the angle, the longer the opposite side. Conversely, the smaller the angle, the shorter the opposite side.

Front

When can you use the Law of Sines?

Back

The Law of Sines can be used in any triangle, especially when you have two angles and one side (AAS or ASA) or two sides and a non-included angle (SSA).

Front

When can 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

What is an ambiguous case in the Law of Sines?

Back

An ambiguous case occurs when using the Law of Sines with the SSA condition, where two different triangles may be possible or no triangle may exist.

Front

How do you round numbers to the nearest hundredths?

Back

To round to the nearest hundredths, look at the third decimal place. If it's 5 or more, round up the second decimal place by one. If it's less than 5, keep the second decimal place the same.

Front

What is the sine of 30 degrees?

Back

The sine of 30 degrees is 0.5.