sine rule

• What is the sign rule used for?

  Finding relationships in triangle sides and angles
• How are the sides of a triangle labeled in the sign rule?

  With lowercase letters a, b, and c
• How are the angles of a triangle labeled in the sign rule?

  With capital letters A, B, and C
• What does the sign rule state about the ratios of sides and angles?

  The ratios are equal for all sides and angles
• If side a is 11 cm and angle A is 85°, how do you express the sign rule?

  a / sin A = b / sin B
• How do you find side X using the sign rule?

  Multiply both sides by sin A
• What is the value of X when calculated from the sign rule?

  19.1 cm
• What should you do if the triangle's corners are labeled with letters?

  Cover or scribble out the labels temporarily
• How do you express the sign rule when finding a missing angle?

  sin A / a = sin B / b
• What is the first step in finding a missing angle using the sign rule?

  Label the sides and angles appropriately
• What happens to the fractions in the sign rule when finding a missing angle?

  They are expressed as reciprocals
• How do you find the value of X after calculating sin X?

  Use the inverse sine function
• What is the approximate value of X when calculated from the sign rule for the last example?

  29.6 cm
• What is the value of sin 88 divided by 25?

  sin 88 / 25
• How do you isolate s of X in the equation?

  Multiply both sides by 18
• What does multiplying by 18 do to the left side of the equation?

  It cancels the divide by 18
• What is the first step to find the value of X after calculating s of X?

  Use the inverse sine function
• What is the rounded value of X after calculating the inverse sine?

  46.0 degrees
• Why do we round the value of X to one decimal place?

  To provide a suitable degree of accuracy
• What is the process to find an angle using the sine rule?

  1. Label the angle and sides.
  2. Write the sine rule formula.
  3. Substitute known values.
  4. Multiply to isolate sine of the angle.
  5. Use inverse sine to find the angle.
• What is the sine rule formula used for finding angles?

  sin A / a = sin B / b
• What do you do after substituting values into the sine rule?

  Multiply both sides by the side length
• What happens if the calculated angle appears obtuse but is less than 90°?

  Check for a second possible angle
• How do you find the second possible angle from the sine value?

  Subtract the first angle from 180°
• What is the second angle if the first angle is 65.2°?

  114.8°
• What does the term "ambiguous case" refer to in triangle problems?

  Two possible angles can satisfy the sine rule
• How can you determine which angle to use in an ambiguous case?

  Look for additional information in the question
• What should an exam question indicate if it involves an obtuse angle?

  It should specify that X is obtuse
• What is the final answer if the question states X is obtuse and the calculated angle is 65.2°?

  114.8°
• What is the final answer if the question states X is acute and the calculated angle is 65.2°?


  65.2°
• What are the key points to remember when solving for angles using the sine rule?

  • Label angles and sides correctly
  • Use the sine rule formula
  • Isolate sine of the angle
  • Consider possible obtuse angles
  • Check for additional information in questions