MODULE 3

• Discipline


  Good taste<|>Excellence
• Writers: Allen O. Aquino, Gemma Y. Bandoquillo
• Cover Illustrator: Joel J. Estudillo
• Department of Education, National Capital Region, SCHOOLS DIVISION OFFICE, MARIKINA CITY
• Angle of Elevation


  Angle from the horizontal to the line of sight of the observer to the object above
• Angle of Depression


  Angle between a horizontal line from the observer and the line of sight to an object that is below the horizontal line
• Line of Sight


  Imaginary line that connects the eye of an observer to the object being observed
• Trigonometric Ratios


  • Sine
  • Cosine
  • Tangent
  • Cosecant
  • Secant
  • Cotangent
• Using a Clinometer


  1. Choose an object to look at

  2. Look at the top of the object through the straw

  3. Record the angle at which you look up
• Angle of Elevation


  Angle between a horizontal line from the observer and the line of sight to an object that is above the horizontal line
• Solving Angle of Elevation

  • Mount Apo in Mindanao rises vertically 1325 feet over a horizontal distance of 4629 feet
  • Guy wire 100 feet long attached to the top of a tree, making an angle of 37° with the ground
  • 22 feet fire truck ladder leaning against a building makes a 70° angle with the ground
• Solving Height


  • Guy wire 100 feet long attached to the top of a tree, making an angle of 37° with the ground
  • 20-foot ladder leaning against a wall so that the base of the ladder is 14 meters from the base of the building
  • Angle of elevation from a car to a 150 ft tower is 32°
  • 5 ft tall man casts a shadow of 6 ft on the ground
  • Angle of elevation of 38° from 14 feet away from a flagpole
• Solving Distance


  • 22 feet fire truck ladder leaning against a building makes a 70° angle with the ground
  • Angle of elevation from a car to a 150 ft tower is 32°
• Riddle: Where are the popular shoes?
• Angle of depression


  Angle measured downward from the horizontal to an object below the observer
• Angle of elevation


  Angle measured upward from the horizontal to an object above the observer
• Shadow


  The dark area or shape produced by a body coming between rays of light and a surface
• Trigonometric ratios


  • Sine
  • Cosine
  • Tangent
• Solving problems using trigonometric ratios

  1. Identify the given information

  2. Identify the unknown

  3. Choose the appropriate trigonometric ratio

  4. Substitute values and solve
• A 15-ft ladder leans against a brick wall. If the foot of the ladder is 6 feet from the wall, find the angle that the ladder makes with the wall to its nearest degree.
• What is asked in the problem?
• What Mathematical equation that can be used to solve the problem?
• What is the solution of the problem?
• What is the answer?
• Encircle the letter of the correct answer.
• Problems

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• Bryant, Merden l.,Bulalayao , Leonides E.Callanta, Merlyn M.,Cruz, Jerry D., De Vera Richard F., Garcia Gilda T.Javier , SoniaE.Lzaro,Roselle A. Mesterio, Bernadette J.& Saladino, Rommel Hero A.(2014) Mathematics 9 Learner's Material, Department of Education, Republic of the Philippines, Vibal Group Publishing Inc., Pasig City
• Common Creatives Images