Sine Relationships in Triangles

The video tutorial explains the derivation of the Law of Sines for triangles. It begins by introducing a triangle with sides a, b, and c, and angles A, B, and C. An altitude is dropped from angle A, forming two right triangles. The sine relationships in these triangles are explored, leading to the derivation of the Law of Sines: sin(A)/a = sin(B)/b = sin(C)/c. The process is repeated for angles A and B, confirming the law. The tutorial concludes with a summary of the Law of Sines.

What are the labels used for the angles opposite the sides of a triangle?

• Numbers 1, 2, 3

• Uppercase A, B, C

• Lowercase a, b, c

• Greek letters alpha, beta, gamma

In the first right triangle, what is the sine of angle B equal to?

• H divided by c

• H divided by h

• H divided by b

• H divided by a

What is the relationship between H, B, and the sine of angle C?

• H equals B times sine of C

• H equals C times sine of B

• H equals A times sine of B

• H equals B times sine of A

Which side is the hypotenuse in the first right triangle?

• Side a

• Side b

• Side c

• Side h

When dropping an altitude from angle C, what new angle is formed in the external triangle?

• 180 degrees minus B

• 180 degrees minus A

• 180 degrees minus C

• 90 degrees

What is the sine of 180 degrees minus A equal to?

• Tangent of A

• Sine of A

• Cotangent of A

• Cosine of A

How is the sine of angle A related to side length a?

• Sine of A minus a

• Sine of A plus a

• Sine of A multiplied by a

• Sine of A divided by a

What is the final expression of the Law of Sines?

• Sine of A divided by a equals sine of B divided by c

• Sine of A divided by a equals sine of B divided by b

• Sine of A divided by a equals sine of C divided by c

• Sine of A divided by a equals sine of B divided by b equals sine of C divided by c

What is the significance of the altitude in deriving the Law of Sines?

• It creates two right triangles

• It divides the triangle into two equal parts

• It is parallel to one of the sides

• It is the longest side of the triangle

What is the relationship between the sine of angle B and side length b?

• Sine of B divided by b

• Sine of B multiplied by b

• Sine of B plus b

• Sine of B minus b