warm up find the following missing values. find the following missing values. 1)2)
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WARM UPWARM UP
Find the following missing values.Find the following missing values.
1)1) 2)2)
35
z
w
200
zw
160
3045
Three Trig. RatiosThree Trig. Ratios
1)1) sinesine2)2) cosinecosine3)3) tangenttangent
Today we are looking at the Today we are looking at the
Sine and CosineSine and Cosine
sine ratiosine ratioleg opposite of opp
sine of ; sin hypotenuse hyp
AA A
A
BCLeg opposite
Hypotenuse
cosine ratioscosine ratiosleg adjacent of adj
cosine of ; cos hypotenuse hyp
AA A
A
BC
Leg adjacent
Hypotenuse
13
5
x
X
Y
b
1.1. Find Find cos Xcos X
2.2. Find Find sin Xsin X
3.3. Find Find cos Ycos Y
4.4. Find Find sin Ysin Y
12
13
We must first find “b”.It’s a Pythagorean Triple! So b = 12
b =
1
25
135
13
12
13
Calculator StuffCalculator Stuff
MAKE SURE YOU ARE MAKE SURE YOU ARE IN IN DEGREEDEGREE MODEMODE EVERY EVERY TIME!!!!!!!!!!!!!!TIME!!!!!!!!!!!!!!
Calculator StuffCalculator StuffFind the missing values.Find the missing values.
5) sin 345) sin 34oo==
6) cos 896) cos 89oo==
7) sin 7) sin ? ? oo = 0.1510 = 0.1510
8) cos 8) cos ? ? oo = .5592 = .5592
0.5591929
0.0174524
Use sin-1 on calc8.68488o
Use cos-1 on calc55.9995o
z
28
y
1000
x
o
9) Find the measure of the missing angles and 9) Find the measure of the missing angles and lengths.lengths.
cos 621000
x
z = 180 – 90 – 28 = 62o
62o
cos62 1000 10001000
x
469.472 x
469
You can use TRIG or PYTHA. THM to find “y”
2 2 2469 1000y 2 2 21000 469y 2 780,039y
2 780,039
883.198
y
y
883
HINT: It is easiest to find the missing value that has two known values…….. In this case find “z” first since you already know two sides.
Find the Find the missing valuesmissing values..10) 10) 2 2 218 30z
z
y
x
1830
2 2 230 18 576z 2 576z
576 24z
24
24cos
30x
1 24cos 36.8699
30
37
o
ox
37o
180- 90 – 37 =
53o53o
Drop the Altitude from the vertex angle B and make two right triangles. Now you can use trig to find the missing angles.
4
55
B
A C
Find the measures of all three Find the measures of all three anglesangles..
2cos
5A
1 2cos
5
1 2cos 66.422
5
66o m A
This is a great problem! Can be very tricky!!!
2 266o 66o
180 – 66 – 66 = 48o
48o
LADDERSLADDERS!!12) A 6 12) A 6 mm ladder reaches ladder reaches
higher up a wall when placed higher up a wall when placed at a 70 degree angle than at a 70 degree angle than when placed at a 60 degree when placed at a 60 degree angle.angle.
How much higher, to the How much higher, to the nearest tenth of a meter?nearest tenth of a meter?
LADDERSLADDERS!!12) A 6 m ladder reaches higher up a wall when placed at a 70 12) A 6 m ladder reaches higher up a wall when placed at a 70
degree angle than when placed at a 60 degree angle.degree angle than when placed at a 60 degree angle.
How much higher, to the nearest tenth of a meter?How much higher, to the nearest tenth of a meter?
70o60o60o6
feet
70o
6 f
eet
LADDERSLADDERS!!12) A 6 m ladder reaches higher up a wall when placed at a 70 degree 12) A 6 m ladder reaches higher up a wall when placed at a 70 degree
angle than when placed at a 60 degree angle.angle than when placed at a 60 degree angle.
How much higher, to the nearest tenth of a meter?How much higher, to the nearest tenth of a meter?
sin 606
y
70o60o
60o
6 fe
et
70o
6 f
eet
xy
sin 706
x0.866
6
y 0.9397
6
x
5.196 ft y 5.6382 ft x
5.6382 – 5.196 = 0.4422 = 0.4 ft
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