Introduction to Trigonometry

Introduction to Trigonometry

Objectives

• Identify the sides of right-angled triangles

• Calculate complementary angle of right-angled triangles

History

The word trigonometry comes from the Greek words trigon (triangle) and metria (measurement).

Originally trigonometry was used as an aid in the study of astronomy.

Name Sides in Right-Angled Triangles

• The Hypotenuse

• The opposite side

• The adjacent side

Complementary Angles

• The three angles in any triangle add to 180°.

• Since one angle in a right-angled triangle measures 90°, the other two angles must add to 90° to make up the 180°.

• The two acute angles in any right-angled triangle are complementary angles (ie add to 90°).

Label Sides

• Use the two CAPITAL letters at its ends.

• Use one lower case letter which matches the opposite vertex (corner).

• Side GH can be called f.

Multiple Choice

The side adjacent to angle

 $\theta$  is ...

• LM

• LN

• MN

Multiple Choice

The hypotenuse is ...

• LM

• LN

• MN

Multiple Choice

What is the name given to the longest side of a right-angled triangle?

• Hypotenuse

• Opposite

• Adjacent

Multiple Choice

The side opposite to angle

 $\theta$  is ...

• LM

• LN

• MN

Multiple Choice

The side ‘next to’ the marked angle is called:

• Hypotenuse

• Touching

• Adjective

• Adjacent

Multiple Choice

Which of the following has the longest side?

• LM

• LN

• MN

Multiple Choice

What is the opposite angle to the side with length 12 m?

• angle A

• angle B

• angle C

Multiple Choice

Which angle must be the right angle for this triangle?

• angle A

• angle B

• angle C

Multiple Choice

Complementary angles add together to give:

• 90⁰

• 180⁰

• 360⁰

Multiple Choice

What is the size of angle P?

• 90⁰

• 24⁰

• 66⁰

• 76⁰

Multiple Choice

What is the size of the missing angle in this triangle?

• 20⁰

• 30⁰

• 90⁰

• 160⁰

Multiple Choice

Insert a capital letter to make this statement true.

Side opposite angle B = Side adjacent to angle ...

• A

• B

• C

Multiple Choice

Choose the response that correctly completes this statement.

The side adjacent to angle R is also:

• adjacent to angle P

• opposite angle P

• opposite angle R

Multiple Choice

What is the complement of 50⁰?

• 90⁰

• 50⁰

• 40⁰

• 30

Multiple Choice

In which of these diagrams are all sides correctly named, with respect to angle P?