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Lesson 3

1. Lesson 3

1.6. Explore 2

Mathematics 20-3 Module 4

Module 4: The Right Kind Of Triangles

 

Self-Check 1
  1. Determine the value of x. Round to one decimal place.

     
    This is an illustration of a triangle. The triangle has a hypotenuse 20 cm long. The side opposite a 38 degree angle is labelled x.

    Answer

  2. Determine the value of θ. Round to the nearest degree.

     
    This is an illustration of a triangle. The hypotenuse of the triangle is 20 cm long. The angle between the hypotenuse and a side of length 9 cm is labelled theta.

    Answer

Next, you will apply the trigonometric ratios in various problem situations. In Try This 3 you will explore the relationship between slope, angle of elevation, and the tangent ratio.

 

Try This 3

 

In areas of Canada with high snowfall, the minimum pitch (slope) for new construction is 6:12, which is said “six twelve.” To the nearest degree, what angle of elevation does the roof make with the horizontal?

 

This is a photo of a house under construction.

iStockphoto/Thinkstock

  1. A pitch or slope of 6 to 12 means the roof rises 6 in to a run of 12 in. Use this information to sketch and label a diagram. hint

  2. Use the slope formula to find the slope of the roof. hint

  3. In the diagram, label the angle of elevation as θ.

  4. Label the adjacent, opposite, and hypotenuse sides in reference to the angle of elevation.

  5. Choose the correct trig ratio to help find θ, the angle of elevation. hint

  6. Compare the tangent ratio you found in question 5 to the slope ratio you found in question 2. What do you notice?

  7. Continue to solve for θ. hint
Share 1

 

Discuss the following question with a partner or with a group of people:

  • Based on question 6 from Try This 3, how would you explain the relationship between slope, angle of elevation, and the tangent ratio?

Create a short paragraph to explain this relationship.

 

course folder Save your responses to Try This 1 and the short paragraph summary from Share 1 in your course folder.

 

If you solved correctly, the angle of elevation should be 27°.
Since you know the opposite and adjacent side lengths, the tangent ratio will work.

This diagram shows a right triangle with a rise of 6 inches and a run of 12 inches.