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Trigonometry

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by

Kelsey Jasmine

on 21 November 2013

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Transcript of Trigonometry

Trigonometry

Opposite
Adjacent
Hypotenuse
30º
θ
SOH CAH TOA
Sin 30°=
Cos 30°=
Tan 30°=
Sine Cosine Tangent
4
12
10
4/12
10/12
4/10
30º
18
x
opp
adj
hyp
Sin30º=x/18

18 x Sin30º= x/18

.'. x= 18 x sin30º

.'. x= 9
x
12
40º
Cos 40º = x/12
12 x Cos40º= x/12
.'.x= 12x Cos40º
.'. x= 9.2
adj
hyp
x
8.4
Tan32º= x/8.4
8.4 x Tan32º= x/8.4
.'. x = Tan32ºx 8.4
.'. x = 5.25
32º
Sin= opp/hyp
Cos= adj/hyp
Tan= opp/adj
opp/hyp
adj/hyp
opp/adj
Lets learn
trigonometry

Problem for you!
3
x
Find x
Did you get...
38°
A mountain is 3km high on one side but how tall is it on the other?
Get a pen and paper to work this out
Tan(38°)= x/3
3x Tan38= x/3
x=3 x Tan38
.'. x = 2.34km
Therefore, the other side of
the mountain is 2.34km.
the side opposite the angle
the side next to the angle
the longest side
the angle of the triangle
John is standing 7 meters away from a tree. The length from the top of the tree to his feet is 11 meters away.
How tall is the tree?
7m
11m
44°
Woohoo!
Good Job!
The Answer is...
Sin44°= x/11
.'.x= 11x Sin44°
.'.x= 7.6m
.'. the Tree is 7.6m tall
not to actual size
The bike and the car are leaving the city but at different speeds. After 1 hour the distance between the city and the bike is 54km away. The angle is 29 degrees. How far away is the bike from the car?
Question no. 3
x
54
19
x
37°
Example: Finding a side
Cos37°= 19/x
19÷ Cos37= 19/x
.'. x= 19÷ Cos37
.'. x= 23.8
*if the x is at the top of the fraction then you have to multiply
*if the x is at the bottom then you have to divide
SOH CAH TOA
Multiply
Divide
Find X
Find X
Find x
Tips
29
ANSWER..........
Cos29°= 54/x
.'. x= 54 ÷ Cos29°
.'. x= 61.74 km
Finding a Side of a right angled
Triangle using Trigonometry
hmmmm
Trigonometry
Finding the angle of this triangle is easy... try this...
12m
15m
You use Tan because you have the opposite and adjacent measurements.

Tan0 = 12/15
Tanˉ (12÷15)
.'. x= 38.7mˉθ
0
Finding the Angle
Question!
What is the Angle?
0
145
100
Full transcript