Transcript right triangles review-eoct

30  60  90



1: 3 : 2
x : x 3 : 2x
Short Leg:Long Leg:Hypotenuse
30-60-90 Right Triangle
60
2
1
30
3
This is our reference triangle for
the 30-60-90 triangle.
We will use a reference triangle
to set up a proportion then solve.
Ex: 2
Solve for x and y
y
a√3
300
x a
2a 24
600
12 3  y
45  45  90



Leg:Leg:Hypotenuse
1:1: 2
x: x: x 2
EX: 3 Solve for x
45
3 a√2
a
a x
3 2
x
2
Opp
Sin 
Hyp
hypotenuse
Adj
Cos 
Hyp
Opp
Tan 
Adj

adjacent
opposite
opposite
Finding a side.
(Figuring out which ratio to use and
getting to use a trig button.)
Ex: 1 Figure out which ratio to use. Find x. Round
to the nearest tenth.
x
tan 55 
20
20 m
55
20 tan 55  x
20
tan
55
)
x  28.6 m
x
Shrink yourself
down and stand
where the angle is.
Now, figure out
which trig ratio
you have and
set up the
problem.
Ex: 2 Find the missing side. Round to the nearest
80
tan 72 
x
x tan 72  80
tenth.
80 ft
80
x
tan 72
72
x
80

(
tan
Shrink yourself down and
stand where the angle is.
72
)
)
=
x  26 ft
Now, figure out which trig ratio
you have and set up the problem.
Ex: 3 Find the missing side. Round to the nearest
tenth.
x
283 m
24
Shrink yourself
down and stand
where the angle is.
Now, figure out
which trig ratio
you have and
set up the
problem.
x
sin 24  
283
283sin 24  x
x  115.1 m
Ex: 4 Find the missing side. Round to the nearest
tenth.
20 ft
40
x
x
cos40  
20
20 cos40  x
x  15.3 ft
Problem-Solving Strategies
B
You are given all 3 sides of the
triangle.
Find the two non-right angles.
25
7
C
1. Use 2 different trig ratios to
get each of the angles.
A
24
24
CosA 
25
1  24 
A  Cos  
 25 
A  16.3
24
TanB 
7
1  24 
B  Tan  
7
B  73.7
Angle
of
Elevation/Depression
Sometimes when we use right triangles to model real-life situations, we
use the terms angle of elevation and angle of depression.
If you are standing on the ground and looking up at a hot air balloon, the
angle that you look up from ground level is called the angle of elevation.
If someone is in the hot air balloon and looks down to the ground to see
you, the angle that they have to lower their eyes, from looking straight
ahead, is called the angle of depression.
Balloon
Angle of
depression
Angle of
elevation
You
Angle of Elevation/Depression
If you look up 15º to see the balloon, then the person in the
balloon has to look down 15º to see you on the ground.
Angle of elevation = Angle of depression.
Balloon
Angle of depression = 15º
Angle of
elevation= 15º
You
Notice that in this situation, the one of the legs that forms the
right angle is also the height of the balloon.
Draw a Picture
When solving math problems, it can be very helpful to
draw a picture of the situation if none is given.
Here is an example.
Find the missing sides and angles for
Triangle FRY. Given that angle Y is
the right angle, f = 68, and y = 88.
F
88
r
The picture helps to visualize what
we know and what we want to find!
Y
R
68