Introduction to basic trigonometry

Introduction to Trigonometry

Objectives

• Identify the sides of right-angled triangles

• Calculate complementary angle of right-angled triangles

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

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

• Hypotenuse

• Opposite

• Adjacent

Multiple Choice

The hypotenuse of triangle LMN is ...

• n

• m

• l

Multiple Choice

The side opposite to angle

$$\theta$$  in triangle LMN is ...

• n

• m

• l

Multiple Choice

The side adjacent to the angle

$$\theta$$  in triangle LMN is ...

• n

• m

• l

Multiple Choice

Which angle must be the right angle for this triangle?

• angle A

• angle B

• angle C

Multiple Choice

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

• angle A

• angle B

• angle C

Multiple Choice

Complementary angles add together to give:

• 90⁰

• 180⁰

• 360⁰

Multiple Choice

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

• 20⁰

• 30⁰

• 90⁰

• 160⁰

Using sin, cos or tan to find the side or angle of a right triangle.

• Identify the sides or angles

• Choose the right trig ratio based on what was given.

• Solve the equation to find the unknown

Trigonometric Ratios

Remember, each of these ratios relies on you identifying the sides of the triangle based on your reference angle.

Multiple Choice

Which ratio represents

$$\cos\left(\angle W\right)$$  ?

• $$\frac{8}{15}$$  

• $$\frac{15}{17}$$  

• $$\frac{8}{17}$$  

Multiple Choice

Which ratio represents

$$\tan\left(\angle W\right)$$  ?

• $$\frac{8}{17}$$  

• $$\frac{15}{17}$$  

• $$\frac{8}{15}$$  

Multiple Choice

Which equation should be used to find the missing side length, x?

• $$\cos\left(33\right)=\frac{x}{14}$$  

• $$\sin\ \left(33\right)=\frac{x}{14}$$  

• $$\tan\ \left(33\right)=\frac{x}{14}$$  

• $$\tan\left(33\right)=\frac{14}{x}$$  

• $$\cos\left(33\right)=\frac{14}{x}$$  

Steps to solving for a missing triangle side:

• Identify which 2 sides are "given"

• Which trig ratio goes with those sides?

• Set up a proportion

• Solve your proportion

Multiple Choice

Find the distance between the ship and the ocean floor (d)

• 18.9 m

• 19.5 m

• 47 m

• 27.5 m