Law of Sines

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

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

Back

To find a missing side, use the formula: a/sin(A) = b/sin(B). Rearrange to find the unknown side: a = b * (sin(A)/sin(B)).

Front

How do you find a missing angle using the Law of Sines?

Back

To find a missing angle, use the formula: sin(A)/a = sin(B)/b. Rearrange to find the unknown angle: A = sin^(-1)(b * (sin(B)/a)).

Front

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

Back

In a triangle, larger angles are opposite longer sides, and smaller angles are opposite shorter sides.

Front

If angle A = 30 degrees and side a = 5, what is the ratio of side a to sin(A)?

Back

The ratio is 5/sin(30 degrees) = 5/0.5 = 10.

Front

If angle B = 45 degrees and side b = 7, what is the ratio of side b to sin(B)?

Back

The ratio is 7/sin(45 degrees) = 7/(√2/2) = 7√2.

Front

What is the sine of 90 degrees?

Back

The sine of 90 degrees is 1.

Front

In triangle ABC, if angle A = 44 degrees and angle B = 36 degrees, what is angle C?

Back

Angle C = 180 - (A + B) = 180 - (44 + 36) = 100 degrees.

Front

If side a = 10 and angle A = 30 degrees, what is side b if angle B = 60 degrees?

Back

Using the Law of Sines: b = a * (sin(B)/sin(A)) = 10 * (sin(60)/sin(30)) = 10 * (√3/2)/(1/2) = 10√3.

Front

What is the sine rule used for?

Back

The sine rule is used to find unknown sides or angles in non-right triangles.