short leg:long leg:hypotenuse. 30-60-90 right triangle 1 2 30 60 this is our reference triangle for...
TRANSCRIPT
906030 2:3:1
Short Leg:Long Leg:Hypotenuse
xxx 2:3:
30-60-90 Right Triangle
12
30
60
This is our reference triangle for the 30-60-90 triangle.
3
We will use a reference triangle to set up a proportion then solve.
600
300
x
24
Solve for x and yEx: 2
2a
a
a√3y
12 3 y
904545 2:1:1
Leg:Leg:Hypotenuse2:: xxx
x
345
EX: 3 Solve for x
x 3 2
2
a√2a
a
oppositehypotenuse
SinOpp
Hyp
adjacent
CosAdj
Hyp
TanOpp
Adj
hypotenuseopposite
adjacent
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.
5520 m
x
20
55tanx
m 6.28x
x55tan20tan 20 55 )
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 tenth.
72
80 ft
x
x
8072tan
ft 26x
8072tan x
72tan
80x
tan 80 72 = ( ) )Shrink yourself down and stand where the angle is.Now, figure out which trig ratio you have and set up the problem.
Ex: 3 Find the missing side. Round to the nearest tenth.
24
283 mx 283
24sinx
m 1.115x
x24sin283Shrink yourself down and stand where the angle is.
Now, figure out which trig ratio you have and set up the problem.
Ex: 4 Find the missing side. Round to the nearest tenth.
4020 ft x
2040cos
x
ft 3.15x
x40cos20
Problem-Solving Strategies
You are given all 3 sides of the triangle.
Find the two non-right angles.
1. Use 2 different trig ratios to get each of the angles.
AC
B
24
257
1 1
24 24
25 724 24
25 7
16.3 73.7
CosA TanB
A Cos B Tan
A B
Angle of Elevation/Depression
Balloon
You
Angle of depression
Angle of elevation
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.
Angle of Elevation/DepressionIf 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.
Notice that in this situation, the one of the legs that forms the right angle is also the height of the balloon.
Angle of elevation = Angle of depression.
Balloon
You
Angle of depression = 15º
Angle of elevation= 15º
Draw a PictureWhen 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.
RY
F
68
88r
The picture helps to visualize what we know and what we want to find!