MODULE 4

• Discipline


  Good taste<|>Excellence
• In this module, you will learn how to use trigonometric ratios to solve real-life problems involving right triangles
• You can say you have understood the lesson if you can

  • Use calculator in solving angles and converting radian to degree and vice versa
  • Solve real life problems involving angle of elevation
  • Solve real life problems involving angle of depression
• Steps to solve problems involving right triangles

  1. Represent the unknown quantity or quantities using a variable or variables

  2. Use the given facts to illustrate the problem

  3. Decide on which of the six trigonometric ratios should be used

  4. Solve the mathematical equation

  5. Check the results
• Trigonometric ratios


  Sine (sin), cosine (cos), tangent (tan) and their reciprocals, cosecant (csc), secant (sec) and cotangent (cot)
• Example 1

  • A 10.97-meter ladder leans against the top of the parapet wall of the CISSL Candazo Building. The bottom of the ladder makes a 60o with the ground. How high is the school building?
• Example 2

  • A southwest monsoon caused an old tree broke into 2 parts forming an angle of 35o with the ground. If the top of the tree touched the ground 15 feet away from the roots of the tree, what was the original height of the tree?
• Example 3

  • A 25-foot electric wire is attached from the top of the post down to a shorter post 14 feet in height. The angle formed between the longer post and the wire attached on the top of this post is 30o. How long is the longer post?
• Right triangle


  A triangle in which one of the angles is a right angle (90 degrees)
• Solving right triangle problems

  1. Identify the given information

  2. Determine the appropriate trigonometric ratio to use

  3. Substitute the given values into the trigonometric ratio equation

  4. Solve for the unknown value
• The problem should involve application of right triangle
• Rubric for Creating Word Problems

  • Appropriate content is used for the word problem
  • Student clearly understands the mathematical concepts
  • The word problem is written in clear and coherent language
  • It is easy to follow and read
• Rubric for the Mathematical Solution


  • The student was able to find all the measures using all the concepts presented
  • The student was able to find the measures using some of the concepts presented
  • The student was able to find some of the measures using any of the mathematical concepts that is not presented
  • The student was able to find some of the measures without using any of the mathematical concepts
  • The student was not able to find any measure
• sin

  Sine - the trigonometric ratio of the opposite side to the hypotenuse of a right triangle
• cos

  Cosine - the trigonometric ratio of the adjacent side to the hypotenuse of a right triangle
• tan

  Tangent - the trigonometric ratio of the opposite side to the adjacent side of a right triangle
• cot

  Cotangent - the reciprocal of the tangent ratio
• The entrance to a parking lot is very dark. One way to brighten it up is to attach a light on top of a 5.8 m pole. The base of the pole is 10 m from the entrance.
• Finding the angle x

  1. Use the trigonometric ratio of sine, cosine, or tangent

  2. Substitute the given values into the equation

  3. Solve for the angle x
• Finding the distance of the top of the pole from the entrance


  1. Use the trigonometric ratio of sine, cosine, or tangent

  2. Substitute the given values into the equation

  3. Solve for the distance
• Engr. Moreno plan to design a truss bridge whose trusses form a right triangle. The 5.81-meter inclined truss form a 60o-angle with the horizontal truss.
• Trigonometric ratio


  The ratios of the sides of a right triangle, such as sine, cosine, and tangent
• Finding the height of the bridge


  1. Identify the appropriate trigonometric ratio to use

  2. Substitute the given values into the equation

  3. Solve for the height
• A ladder is placed against a wall such that it reaches the top of the wall. The foot of the ladder is 1.5 meters away from the wall and the ladder is inclined at angle of 50o.
• Finding the length of the ladder

  1. Identify the appropriate trigonometric ratio to use

  2. Substitute the given values into the equation

  3. Solve for the length of the ladder
• A rafter is any parallel beams that support a roof. If the rafter is 4 meters long and makes an angle of 35o with the horizontal, what is the height of the rafter's peak?
• Rafter


  A parallel beam that supports a roof
• Finding the height of the rafter's peak


  1. Identify the appropriate right triangle

  2. Use the trigonometric ratio of sine, cosine, or tangent

  3. Substitute the given values into the equation

  4. Solve for the height of the rafter's peak
• Marikit-na is a female statue in Marikina River Park with a height of 40 ft. If the shadow of the statue on the ground formed is of the same length as its height, what angle is formed from the top of the statue to the tip of the shadow?
• Finding the angle formed from the top of the statue to the tip of the shadow

  1. Identify the appropriate trigonometric ratio to use

  2. Substitute the given values into the equation

  3. Solve for the angle
• Ron flies a kite 4 feet off the ground with 300 feet of string. There is 64 km/hr wind and the string of the kite forms a 29o with the horizontal.
• Identifying the part of the right triangle represented by the 300 feet string


  Determine if the 300 feet string is the adjacent side, opposite side, or hypotenuse of the right triangle
• Finding the height of the kite from the ground

  1. Use the trigonometric ratio of sine, cosine, or tangent

  2. Substitute the given values into the equation

  3. Solve for the height
• Standing across the street 50 feet from the building, the angle to the top of the building is 40o. An antenna sits on the front edge of the building. The angle to the top of the antenna is 52o.
• Finding the height of the building

  1. Use the trigonometric ratio of sine, cosine, or tangent

  2. Substitute the given values into the equation

  3. Solve for the height of the building
• Finding the height of the antenna

  1. Use the trigonometric ratio of sine, cosine, or tangent

  2. Substitute the given values into the equation

  3. Solve for the height of the antenna