Download Finding sides and angles.notebook

Finding sides and angles.notebook
Trig Functions QS
Grade:10
Subject:Geometry
Date:Mar 09
Right angle triangles have special
ratios we can use to find
• missing sides
• missing angles
Finding sides and angles.notebook
First, check that we have a right
angle triangle
Label the sides in relation to on of
the two angles that are NOT 90o
opposite
hypotenuse
adjacent
Finding sides and angles.notebook
Label the sides in relation to on of
the two angles that are NOT 90o
OR
hypotenuse
adjacent
opposite
The hypotenuse will always be across
from the 90o angle
we must identify the angle in question
and label the two sides opposite and
attached.
How do we know?
Finding sides and angles.notebook
There are 3 trigonometric ratios
sine of an angle = opposite side
hypotenuse
cosine of an angle = adjacent side
hypotenuse
tangent of an angle = opposite side
adjacent side
"nick names"
SOH CAH TOA
sin θ = opp/hyp
S O/H
cos θ = adj/hyp
C A/H
tan θ = opp/adj
T O/A
Finding sides and angles.notebook
complete the trig ratios for the angle A
5
A
3
Sin
Cos
4
Tan
1
In this triangle the side opposite <A is 3.
True
False
B
5
3
C
4
A
Finding sides and angles.notebook
2
In this triangle find sine A.
Round to 4 decimal places.
B
5
3
4
C
3
A
In this triangle find Tan B. Round to the four decimal
places if needed.
A 0.75
C 1.3333
B .8050
D 0.6
B
5
3
C
4
A
Finding sides and angles.notebook
Finding a side
Label the sides of the triangle
Set up a ratio with the unknown side (try to put it on the
top of the fraction: the numerator)
B
25
30o
C
4
x
A
Find the height of this tree to the nearest tenth.
Tan 35o =
opp
/
adj
= x/20
x
35o
20 m
Finding sides and angles.notebook
Finding an angle
Label the sides of the triangle
Set up a ratio with the unknown angle
B
θ
25
15
A
C
5
What is the angle of descent for the airplane that
is approaching the airport, at 5000 ft up, and
20,000 feet away.
A
3.93o
B
14.0o
C
5,000 ft
17.4o
xo
20,000 ft
D
75.96o
Finding sides and angles.notebook
You want to build a wheelchair ramp into
your house, it has to go up 6 feet, and the
maximum angle is 5o.
6
How far from the house must
the ramp start ?
6 ft
x
7
Find the angle of this roof.
12
xo
15
5o
Finding sides and angles.notebook
8
Which formula uses 15 and 30 to find angle A?
A
Sine
B Cosine
C
Tangent
D
Pythagorean Theorem
A
30
26
C
9
15
B
Find the measure of angle B?
A
30
26
C
15
B
Finding sides and angles.notebook
10 Find the measure of angle A?
Round to the nearest whole number.
A
30
B 60
C
90
D
45
A
30
26
C
15
Things to remember about triangles
All the angles add up to 180o
Trig and pythagorus only work for
right angle triangles
Area = b x h
2
Area = √(s)(s-a)(s-b)(s-c)
B