WK 11 PreCal - Law of Sines (AAS & ASA)

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 an unknown side using the Law of Sines?

Back

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

Front

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

Back

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

Front

What is the significance of AAS in triangle calculations?

Back

AAS (Angle-Angle-Side) allows you to determine the remaining side and angle of a triangle when two angles and a non-included side are known.

Front

What is the significance of ASA in triangle calculations?

Back

ASA (Angle-Side-Angle) allows you to determine the remaining side and angle of a triangle when two angles and the included side are known.

Front

If angle A = 25° and side a = 32.96, how do you find side b?

Back

Use the Law of Sines: b = a * (sin(B)/sin(A)). First, find angle B using the triangle sum property.

Front

If angle A = 25° and angle B = 42°, how do you find angle C?

Back

Use the triangle sum property: C = 180° - A - B.

Front

What is the formula to find 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

How do you determine if a triangle is possible with given angles?

Back

The sum of the angles in a triangle must equal 180°. If the sum exceeds 180°, the triangle is not possible.

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.