Law of Sine and 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

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).

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

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

Back

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

Front

How do you find an unknown angle using the Law of Cosines?

Back

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

Front

What is the relationship between the sides and angles 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

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, it is a right triangle because 7² + 24² = 25².