Transcript Trig powerpoint

Trigonometry
Right-Angled triangles
© Rosemary Vellar
Why
trig?
Labeling
sides
Trig ratios
Calculator
use
side
angle
Instructions for use

sin
information slides
side
angle
cos

side
angle
tan
side
angle
There are 9 worked examples shown in this PowerPoint plus
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.
3
1 2
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© Rosemary Vellar
Why
trig?
Labeling
sides
Trig ratios
Calculator
use
side
angle
sin
side
angle
cos
side
angle
tan
side
angle
3
1 2
Trigonometry: What is it used for?

To find the length of a side

To find the size of an angle

Some practical uses include:
x

– Navigation (e.g., finding lost ships)
– Construction industry
• Finding heights of buildings
• Finding pitch of a roof
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© Rosemary Vellar
Why
trig?
Labeling
sides
Labeling the sides
Trig ratios
Calculator
use
side
angle
The opposite is
opposite the
labeled angle
The hypotenuse
is opposite the
right-angle
sin
side
angle
cos
side
angle

tan
The adjacent is
the side next to
the labeled angle
side
angle
3
1 2
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© Rosemary Vellar
Why
trig?
Labeling
sides
The trigonometric ratios
Trig ratios
Calculator
use
side
angle
sin
side
angle
cos
side
angle
tan
side
angle
3
1 2
The
opposite
sin  
hypotenuse
trigonometric
ratios, sin, cos,
adjacent
cos  
hypotenuse
tan are used
when comparing
particular side
opposite
tan  
adjacent
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lengths.
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slide
© Rosemary Vellar
Why
trig?
Labeling
sides
Calculator work (side length)
Trig ratios
Calculator
use
side
angle
Question:
Evaluate:
1
Answer:
2
sin 30
sin
Calculator steps: Sin30=
cos
Refers to
the length on
the opposite
side
angle
side
angle
tan
side
angle
3
1 2
1
sin 30 
2

Refers to the
length on the
hypotenuse
Refers to
the angle in
the triangle
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1
2
30o
© Rosemary Vellar
Why
trig?
Labeling
sides
Trig ratios
Calculator
use
side
angle
sin
Calculator work (angle size)
Question:
Find  if tan  =¼
Calculator steps: shift tan (1/4)=
side
angle
cos
side
angle
tan
side
angle
3
1 2
Answer:
14.036…=14o (2 sig figs)
Refers to
the length on
the opposite
1
tan 14 
4

Refers to the
length on the
adjacent
Refers to
the angle in
the triangle
1
14o
4
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© Rosemary Vellar
Why
trig?
Labeling
sides
Sine (Side length)
Trig ratios
Calculator
use
side
angle
5
Find the value of
the unknown side.
x
25o
sin
side
angle
cos
side
angle
Step 1: Decide which trig ratio to
use and set up the trig equation.
x
sin 25 
5
Step 2: Rearrange the equation.
x  5 sin 25
Step 3: Use calculator to evaluate.
x  5  sin 25
tan
side
angle
3
1 2
opposite
hypotenuse
x  2.1 cm 2 sig . fig 
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© Rosemary Vellar
Why
trig?
Labeling
sides
Sine (Angle size)
Trig ratios
Calculator
use
side
angle
Find the value of
the unknown
angle.
5
3

sin
opposite
side
angle
cos
Step 1: Decide which trig ratio to
use and set up the trig equation.
sin  
3
5
tan
Step 2: Use calculator to evaluate.
  37
(nearest degree)
side
angle
side
angle
3
1 2
shift sin (3/5) =
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hypotenuse
© Rosemary Vellar
Why
trig?
Labeling
sides
Cosine (Side length)
Trig ratios
Calculator
use
side
angle
Find the value of
the unknown side.
x
40o
10
adjacent
sin
side
angle
cos
side
angle
tan
side
angle
3
1 2
Step 1: Decide which trig ratio to
use and set up the trig equation.
Step 2: Rearrange the equation.
x
cos 40 
10
x  10 cos 40
hypotenuse
Step 3: Use calculator to evaluate. x  10  cos 40
x  7.7 cm 2 sig . fig 
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© Rosemary Vellar
Why
trig?
Labeling
sides
Cosine (Angle size)
Trig ratios
Calculator
use
side
angle
Find the value of
the unknown
angle.
9

sin
4.6
adjacent
side
angle
cos
Step 1: Decide which trig ratio to
use and set up the trig equation.
tan
Step 2: Use calculator to evaluate.
side
angle
side
angle
3
1 2
cos  
shift cos (4.69) =
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  59
4 .6
9
hypotenuse
(nearest degree)
© Rosemary Vellar
Why
trig?
Labeling
sides
Tan (Side length)
x
Trig ratios
Calculator
use
side
angle
sin
55o
Find the value of
the unknown side.
6
6
tan 55 
x
side
angle
Step 1: Decide which trig ratio to
use and set up the trig equation.
cos
Step 2: Rearrange the equation.
x tan 55  6
6
x
tan 55
Step 3: Use calculator to evaluate.
x  6  tan 55
side
angle
tan
side
angle
3
1 2
opposite
adjacent
x  4.2 cm 2 sig . fig 
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© Rosemary Vellar
Why
trig?
Labeling
sides
Tangent (Angle size)
Trig ratios
Calculator
use
side
angle
8.2
Find the value of
the unknown
angle.

4.6
sin
opposite
side
angle
cos
Step 1: Decide which trig ratio to
use and set up the trig equation.
tan
Step 2: Use calculator to evaluate.
side
angle
side
angle
3
1 2
tan  
shift tan (4.68.2) =
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  29
4 .6
8 .2
adjacent
(nearest degree)
© Rosemary Vellar
Why
trig?
Labeling
sides
Trig ratios
Calculator
use
side
angle
sin
side
angle
Challenge 1
What angle will a 5 m ladder make with the
ground if it is to reach 4.4 m up a wall?
cos
side
angle
tan
side
angle
3
1 2
5
Step 1: Draw a diagram with the
given information.
4.4

Step 2: Decide which trig ratio to
use.
4 .4
sin  
5
Step 3: Solve the trig equation.
  62 (nearest degree)
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© Rosemary Vellar
Why
trig?
Labeling
sides
Trig ratios
Calculator
use
side
angle
sin
side
angle
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.
24 m
Step 1: Draw a diagram with the
given information.
cos
side
angle
tan
side
angle
3
1 2
x
x
cos 17 
24
Step 2: Decide which trig ratio to
use.
x  24 cos 17
Step 3: Solve the trig equation.
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170
x  23 m
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slide
(nearest metre)
Why
trig?
Labeling
sides
Trig ratios
Calculator
use
side
angle
sin
side
angle
cos
side
angle
tan
side
angle
3
1 2
© Rosemary Vellar
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.
Step 1: Draw a diagram
with the given information.
2.2
2.2
40o
40o
y
Step 2: Create a right
angled triangle.
Step 3: Decide which
trig ratio to use.
Step 4: Solve the
trig equation.
x
2.2
tan 40 
y
y
2.2
tan 40
y  2.6 m (1 dec. pl )
 x  5.2 m
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© Rosemary Vellar
Why
trig?
Labeling
sides
Trig ratios
Calculator
use
side
angle
Last slide
sin
side
angle
cos
side
angle
Use the navigation buttons to
repeat selected slides.
tan
side
angle
3
1 2
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