HW14 Law of Sines

What is the Law of Sines?

• 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.

• The Law of Sines is a theorem that applies only to right triangles.

• The Law of Sines states that the sum of the angles in a triangle is equal to 180 degrees.

• The Law of Sines is used to calculate the area of a triangle.

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

• 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.

• Add the angles of the triangle and subtract from 180 degrees to find the missing angle.

• Use the cosine rule to find the length of the opposite side, then apply the sine function.

• Multiply the lengths of the sides by the sine of the known angles to find the missing angle.

What is the sine of 60 degrees?

• 0.500

• 0.707

• 0.866

• 0.933

What is the formula for the Law of Sines?

• a/sin(A) = b/sin(B) = c/sin(C)

• a + b + c = 180°

• c^2 = a^2 + b^2 - 2ab*cos(C)

• sin(A) = sin(B) = sin(C)

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

• It is used to calculate the area of triangles only.

• It allows for the calculation of unknown sides and angles in non-right triangles.

• It is only applicable to right triangles.

• It simplifies the process of adding angles in a triangle.

When can the Law of Sines be applied?

• In any triangle when you know two angles and one side (AAS or ASA) or two sides and a non-included angle (SSA).

• Only in right triangles when you know one angle and one side.

• In any triangle when you know all three sides (SSS).

• Only in isosceles triangles when you know the base angles.

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

• Larger angles are opposite shorter sides, and smaller angles are opposite longer sides.

• Larger angles are opposite longer sides, and smaller angles are opposite shorter sides.

• All sides are equal to their opposite angles.

• The sum of the angles is always greater than the sum of the sides.

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

• Round to the nearest whole number by looking at the digit in the tenths place.

• Round to the specified decimal place, typically to the tenths, by looking at the digit in the hundredths place.

• Always round up regardless of the digit in the next place.

• Round to the nearest hundredth by looking at the digit in the thousandths place.

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

• 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.

• Using the Law of Cosines: B = cos^(-1)((a^2 + b^2 - c^2) / (2ab)).

• Using the Pythagorean theorem to find angle B: B = sqrt(a^2 + b^2).

• Using the tangent function: tan(B) = opposite/adjacent.

What is the sine of 30 degrees?

• 0.5

• 0.25

• 0.75

• 1.0