HW14 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 use the Law of Sines to find a missing angle?

Back

To find a missing angle using the Law of Sines, rearrange the formula to isolate the sine of the angle: sin(A) = a * sin(B) / b, then use the inverse sine function to find the angle.

Front

What is the formula for the Law of Sines?

Back

The formula for the Law of Sines is: a/sin(A) = b/sin(B) = c/sin(C), where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the angles opposite those sides.

Front

What is the significance of the Law of Sines in solving triangles?

Back

The Law of Sines is significant because it allows for the calculation of unknown sides and angles in non-right triangles, making it essential for solving various geometric problems.

Front

When can the Law of Sines be applied?

Back

The Law of Sines can be applied in any triangle, especially when you know either two angles and one side (AAS or ASA) or two sides and a non-included angle (SSA).

Front

What is the relationship between the sides and angles in a triangle according to the Law of Sines?

Back

According to the Law of Sines, larger angles are opposite longer sides, and smaller angles are opposite shorter sides.

Front

How do you round answers in the context of the Law of Sines?

Back

When rounding answers in the context of the Law of Sines, round to the specified decimal place, typically to the tenths, by looking at the digit in the hundredths place.

Front

If a = 8, A = 30°, and b = 10, how do you find angle B?

Back

Using the Law of Sines: sin(B) = b * sin(A) / a. Plugging in the values: sin(B) = 10 * sin(30°) / 8. Calculate sin(B) and then use the inverse sine to find angle B.

Front

What is the sine of 30 degrees?

Back

The sine of 30 degrees is 0.5.

Front

If angle A = 45° and angle B = 60°, what is angle C?

Back

Angle C can be found using the triangle sum property: C = 180° - A - B = 180° - 45° - 60° = 75°.