Geometry (ACT Prep) - 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

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

How do you find the length of a side using the Law of Sines?

Back

To find a side length, use the formula: a = b * (Sin(A)/Sin(B)), where A and B are the angles opposite sides a and b.

Front

How do you find an angle using the Law of Sines?

Back

To find an angle, rearrange the Law of Sines: A = sin⁻¹(a * Sin(B)/b).

Front

What is the formula for 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

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

Back

In any triangle, the larger the angle, the longer the side opposite that angle.

Front

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

Back

In a right triangle, the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse: Sin(θ) = Opposite/Hypotenuse.

Front

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

Back

In a right triangle, the cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse: Cos(θ) = Adjacent/Hypotenuse.

Front

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

Back

In a right triangle, the tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side: Tan(θ) = Opposite/Adjacent.

Front

How do you determine if a triangle is solvable with the Law of Sines?

Back

A triangle is solvable with the Law of Sines if you have at least one side and its opposite angle, or two angles and one side.