1. Module 7

1.12. Page 2

Mathematics 10-3 Module 7 Lesson 3

Module 7: Trigonometry

 

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In this example you will review the names of the sides of a right triangle relative to one of its acute angles. When an acute angle is specified in a right triangle, the acute angle is referred to as the reference angle.

 

Example 1

 

This illustration shows right triangle PQR with angle Q marked as a right angle.

  1. Label the sides of ΔPQR using the letters p, q, and r.
  2. In relation to ∠R, which side is the side opposite? Which is the side adjacent? Which is the hypotenuse?
  3. In relation to ∠P, which side is the side opposite? Which is the side adjacent? Which is the hypotenuse?
  4. Regardless of which acute angle is the reference angle, which side always has the same name or label?

Solution

  1. Side p is across from ∠P. Side r is across from ∠R. Side q is across from ∠Q.

     
    This illustration shows right triangle PQR with angle Q marked as a right angle. Side PQ, which is opposite angle R, is labelled r. Side PR, which is opposite angle Q, is labelled q. Side QR, which is opposite angle P, is labelled p.

  2. In relation to ∠R, side r is the side opposite, side p is the side adjacent, and side q is the hypotenuse.

  3. In relation to ∠P, side p is the side opposite, side r is the side adjacent, and side q is the hypotenuse.

  4. Side q, the longest side, is always the hypotenuse.

Self-Check

 

Try these questions. Use the following diagram.

 

 

This illustration shows right triangle ABC with angle B marked as a right angle. Side AC is 13 centimetres in length. Side AB is 5 centimetres in length. Side BC is 12 centimetres in length.

 

SC 1. What single letter could be used to name side AC? Side BC? Side AB?

 

SC 2. What is the length of the side opposite ∠A? The side adjacent to ∠A?

 

SC 3. What is the length of the side opposite ∠C? The side adjacent to ∠C?

 

SC 4. What is the length of the hypotenuse?

 

Compare your answers.