MODULE 6

• Discipline

  Good Taste<|>Excellence
• Writers: Chonaylon L. Tecson, Amor G. Agarro
• Cover Illustrator: Joel J. Estudillo
• This is a Mathematics module for Grade 9 students on Solving Problems Involving Oblique Triangles
• Learning Objectives

  • Illustrate problems involving oblique triangles
  • Solve problems involving oblique triangles
• Steps to solve problems involving oblique triangles

  1. Read and analyze the problem

  2. Identify essential quantities

  3. Illustrate the problem by sketching/drawing

  4. Use appropriate equation/formula to solve
• Laws of Sines or Laws of Cosines are used to solve problems involving oblique triangles
• If given two sides and an included angle, use Laws of Cosines. If given three sides, use Laws of Sines.
• Distance between home and workplace

  Factor for job satisfaction
• Oblique triangle


  A triangle where none of the angles are right angles
• Problems involving oblique triangles


  • Cruz family in the park
  • Siblings during COVID-19 pandemic
• Knowledge of Laws of Sines and Cosines is useful in dealing with problems involving oblique triangles
• Triangular lot


  Three sides measuring 15 m, 19 m and 29 m<|>Angles opposite each side measuring 27°, 35° and 118° respectively
• Solving the problem


  1. Identify essential quantities

  2. Use an appropriate equation or formula to solve the unknown value or quantity
• The three sides of the lot measure 15 m, 19 m and 29 m
• The angles opposite each side measure 27°, 35° and 118° respectively
• Two sides of a triangle measure 15 m and 18 m, and the included angle formed by these two sides is 65°
• Appropriate equation to use


  c = √(152 + 182 - 2(15)(18)cos65°)
• The third side of the triangle measures 17 m
• The third side of the triangle measures 11 m when the included angle is 38°
• The distance from teacher's house (T) to school (S) is 40 m and the school (S) is 25 m away from learner's house (L)
• The angle between the segment connecting the learner's house to teacher's house and segment connecting the learner's house to the school is 50°
• The distance from teacher's house to learner's house is 52 m
• The school (S) is nearer to the learner's house (L) than the teacher's house (T)
• A tree in front of a house is slightly tilted at 75°, the house is 64 feet away from the tree, and the angle formed from the house to the top of the tree is 40°
• The angle formed from Chloe (C) to Ana (A) to Ben's (B) place is 88 degrees, the angle from Ben to Chloe to Ana is 65 degrees, and Chloe is sitting 125 cm away from Ana
• Chloe is 132 cm away from Ben
• Ana is 117 cm away from Ben
• Chloe is closer to Ben than to Ana
• The measure of angle BAC is 110 degrees and the measure of angle BCA is 48 degrees
• The distance between Ana's and Beth's house is 21.1 m
• Equation to find the distance between Ana's and Carla's house

  a/sin C = c/sin A
• The distance between Ana's and Carla's house is 12.5 m
• Equation to find the distance between Ana's and Ben's house

  a/sine C = c/sine A
• The electric post with base (P) 5.4 m away from John's house (J) is found tilted towards it at 75°
• The distance between the top of the post (T) and John's house (J) is 7.3 m
• Equation to find the distance between the top of the post and John's house


  p = √(j2 + t2 - 2 jt cos P)
• Equation to find the angle opposite the segment connecting the top and the base of the post

  t/sin T = p/sin P