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Trigonometry. Right-Angled triangles. Instructions for use. There are 9 worked examples shown in this PowerPoint plus information slides A red dot will appear top right of screen to proceed to the next slide.

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trigonometry

Trigonometry

Right-Angled triangles

instructions for use
Instructions for use
  • There are 9 worked examples shown in this PowerPoint plus information slides
  • A red dot will appear top right of screen to proceed to the next slide.
  • Click on either the navigation bars below or to the left of screen to access the relevant slides.
trigonometry what is it used for
Trigonometry: What is it used for?
  • To find the length of a side
  • Some practical uses include:
    • Navigation (e.g., finding lost ships)
    • Construction industry
      • Finding heights of buildings
      • Finding pitch of a roof

x

  • To find the size of an angle

labeling the sides
Labeling the sides

The opposite is opposite the labeled angle

The hypotenuse is opposite the right-angle

hypotenuse

opposite

adjacent

The adjacent is the side next to the labeled angle

the trigonometric ratios
The trigonometric ratios

The trigonometric ratios, sin, cos, tan are used when comparing particular side lengths.

calculator work side length

Question:

Evaluate:

Refers to the length on the opposite

Answer:

2

1

Refers to the length on the hypotenuse

Refers to the angle in the triangle

30o

Calculator work (side length)

Calculator steps: Sin30=

So!

calculator work angle size

Refers to the length on the opposite

1

Refers to the length on the adjacent

14o

Refers to the angle in the triangle

4

Calculator work (angle size)

Question:

Answer: 14.036…=14o (2 sig figs)

Find  if tan  =¼

Calculator steps: shift tan (1/4)=

So!

sine side length

5

x

25o

opposite

hypotenuse

Sine (Side length)

Find the value of the unknown side.

Step 1: Decide which trig ratio to use and set up the trig equation.

Step 2: Rearrange the equation.

Step 3: Use calculator to evaluate.

sine angle size

5

3

opposite

hypotenuse

(nearest degree)

Sine (Angle size)

Find the value of the unknown angle.

Step 1: Decide which trig ratio to use and set up the trig equation.

Step 2: Use calculator to evaluate.

shift sin (3/5) =

cosine side length

adjacent

hypotenuse

Cosine (Side length)

10

40o

Find the value of the unknown side.

x

Step 1: Decide which trig ratio to use and set up the trig equation.

Step 2: Rearrange the equation.

Step 3: Use calculator to evaluate.

cosine angle size

adjacent

hypotenuse

(nearest degree)

Cosine (Angle size)

Find the value of the unknown angle.

4.6

9

Step 1: Decide which trig ratio to use and set up the trig equation.

Step 2: Use calculator to evaluate.

shift cos (4.69) =

tan side length

opposite

adjacent

Tan (Side length)

x

55o

Find the value of the unknown side.

6

Step 1: Decide which trig ratio to use and set up the trig equation.

Step 2: Rearrange the equation.

Step 3: Use calculator to evaluate.

tangent angle size

opposite

adjacent

(nearest degree)

Tangent (Angle size)

8.2

Find the value of the unknown angle.

4.6

Step 1: Decide which trig ratio to use and set up the trig equation.

Step 2: Use calculator to evaluate.

shift tan (4.68.2) =

challenge 1

5

4.4

Challenge 1

What angle will a 5 m ladder make with the ground if it is to reach 4.4 m up a wall?

Step 1: Draw a diagram with the given information.

Step 2: Decide which trig ratio to use.

Step 3: Solve the trig equation.

(nearest degree)

challenge 2

170

24 m

x

Challenge 2

A kite is flying on the end of a string which is 24 m long. If the string makes an angle of 17o with the vertical, find the height of the kite above the ground.

Step 1: Draw a diagram with the given information.

Step 2: Decide which trig ratio to use.

Step 3: Solve the trig equation.

(nearest metre)

challenge 3

2.2

40o

40o

y

x

Challenge 3

A roof is in the shape of an isosceles triangle. The pitch of the roof is 40o and the height of the roof is 2.2m. Find the length of the base of the roof.

2.2

Step 1: Draw a diagram with the given information.

Step 2: Create a right angled triangle.

Step 3: Decide which trig ratio to use.

Step 4: Solve the trig equation.

slide17

Last slide

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