day_1_sohcahtoa_intro.ppt grade 9 power point

1. Warm – up: Find the missing measures.
Write all answers in radical form.
45°
45°
x
w
7
60°
30°
10
y
z

2. The Trigonometric Functions
we will be looking at
SINE
COSINE
TANGENT

3. The Trigonometric Functions
SINE
COSINE
TANGENT

4. SINE
Prounounced
“sign”

5. Prounounced
“co-sign”
COSINE

6. Prounounced
“tan-gent”
TANGENT

7. Prounounced
“theta”
Greek Letter

Represents an unknown
angle

8. 
opposite
hypotenuse
Sin
Opp
Hyp

adjacent
Cos
Adj
Hyp

Tan
Opp
Adj

hypotenuse
opposite
adjacent
(SOH)
(CAH)
(TOA)

9. What’s the purpose of SOH CAH
TOA?
The Sine, Cosine and Tangent functions express
the ratios of sides of a right triangle.
We use this to find missing angles.
We can find an unknown angle in a right-angled
triangle, as long as we know the lengths of two of its
sides.
The function takes an angle and gives us the ratio, and
the inverse function takes the ratio to give us the angle

10. We need a way
to remember
all of these
ratios…

11. Old Hippie
Some
Old
Hippie
Came
A
Hoppin’
Through
Our
Apartment

12. SOHCAHTOA
Old Hippie
Sin
Opp
Hyp
Cos
Adj
Hyp
Tan
Opp
Adj

13. Finding sin, cos, and tan

14. 
6
8
10
SOHCAHTOA
10
8
10
6
6
8
Opp
Hyp
Cos
Adj
Hyp
 
Tan
Opp
Adj
 

4
5

3
5

4
3
Sin =

15. Find the sine, the cosine, and the tangent of angle A.
Give a fraction and decimal answer (round to 4 places).
hypo
opp
A 
sin
8
.
10
9
 8333
.

hypo
adj
A 
cos
8
.
10
6
 5555
.

adj
opp
A 
tan
6
9
 5
.
1

9
6
10.8
A

16. Find the values of the three trigonometric functions of .
4
3
? Pythagorean Theorem:
(3)² + (4)² = c²
5 = c
opp
hyp

4
5

adj
hyp

3
5

opp
adj

4
3


sin  cos tan
5

17. Find the sine, the cosine, and the tangent of angle A
A
24.5
23.1
8.2
hypo
opp
A 
sin
5
.
24
2
.
8
 3347
.

hypo
adj
A 
cos
5
.
24
1
.
23

9429
.

adj
opp
A 
tan
1
.
23
2
.
8
 3550
.

B Give a fraction and
decimal answer (round
to 4 decimal places).

18. Now, find the actual measurement of angle A by using
the inverse
A
24.5
23.1
8.2 B
STOP: Make sure Mode
on your calculator is set
to “Degree” not “Radian”
sin-1
(8.2/24.5)= 19.6 degrees
cos-1
(23.1/24.5)= 19.5 degrees
tan-1
(8.2/23.1)= 19.5 degrees
Check: Does it make sense? Lets check Angle B:
sin-1
(23.1/24.5)= 70.5 degrees
70.5 + 19.5 + 90 = 180 degrees. That works!
No matter how you do it, you should
get the same answer (and because we
have all 3 sides, it doesn’t matter
which we choose)

19. Finding a side

20. A surveyor is standing 50 feet from the base of a
large tree. The surveyor measures the non-right
angle from the ground to the top of the tree as
71.5°. How tall is the tree?
50
71.5°
?
tan 71.5°
tan 71.5°
50
y

y = 50 (tan 71.5°)
y = 50 (2.98868)
149.4
y ft

Ex.

21. A person is 200 yards from a river. Rather than walk
directly to the river, the person walks along a straight
path to the river’s edge at a 60° angle. How far must
the person walk to reach the river’s edge?
200
x
Ex. 2
60°
cos 60°
x (cos 60°) = 200
x
X = 400 yards