Q-6.1-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 remember the trigonometric ratios?

Back

Soh Cah Toa: Soh = Sine = Opposite/Hypotenuse, Cah = Cosine = Adjacent/Hypotenuse, Toa = Tangent = Opposite/Adjacent.

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

If angle A is 78 degrees, what is the sine of angle A?

Back

sin(78°) = Opposite side / Hypotenuse.

Front

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

Back

To find a side, rearrange the Law of Sines: a = b * (sin(A) / sin(B)).

Front

What is the measure of angle A if side a = 10, side b = 14, and side A = 50 degrees?

Back

Use the Law of Sines: sin(A) = (a * sin(B)) / b.

Front

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

Back

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

Front

How do you calculate 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 cosine rule?

Back

The cosine rule relates the lengths of the sides of a triangle to the cosine of one of its angles: c² = a² + b² - 2ab * cos(C).

Front

If angle B is 60 degrees and side b is 12, how do you find side a?

Back

Use the Law of Sines: a = b * (sin(A) / sin(B)).