4.8 applications and models using trigonometry. given one side and an acute angle of a right...
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4.8 Applications and Models using Trigonometry
Given one side and an acute angle of a right triangle
Find the remaining parts of the triangle.
A
B
C
90
___
9.45
Cm
Bm
Am
___
8.12
____
c
b
a
Given one side and an acute angle of a right triangle
Find the remaining parts of the triangle.
A
B
C5.49
8.12
4.18
9.45
8.12
8.129.45
c
Cosc
cCos
Given one side and an acute angle of a right triangle
Find the remaining parts of the triangle.
A
B
C5.49
8.12
4.18
2.13
9.458.12
8.129.45
a
aTan
aTan
Given one side and an acute angle of a right triangle
Find the remaining parts of the triangle.
For Angle B
A
B
C5.49
8.12
4.182.13 1.449.4590
Find of an object in the distance
Finding the height of a tree on a mountain.
M
T
2258
ft1000
Find of an object in the distance
Finding the height of a tree on a mountain.
M
T
2258
ft1000
M
MTan
MTan
03.404
221000
100022
Find of an object in the distance
Finding the height of a tree on a mountain.
M
T
2258
ft1000
M
MTan
MTan
03.404
221000
100022
Tft
TTan
TMTan
3.1196
03.404581000
100058
Trigonometry and Bearings
Bearing is an acute angle based off the North - South line. N 38º W
N
S
W E
38
A nautical problem
A yacht is going 14 knots East for 3 hours, then turns N 42º E for an hour. How far from port is the yacht.
42
A nautical problem
Need to find a hypotenuse of a larger triangle. To find the distance.
42
A nautical problem
The extension helps us find the hypotenuse.
We have a few angles and the distance to add.
42
A nautical problem
The extension helps us find the hypotenuse.
We have a few angles and the distance to add.
42
42)3(14
14
48b
a
A nautical problem
The extension helps us find the hypotenuse.
We have a few angles and the distance to add.
42
42)3(14
14
48b
a
a
aSin
aSin
4.10
4814
1448
A nautical problem
The extension helps us find the hypotenuse.
We have a few angles and the distance to add.
42
42)3(14
14
48b
4.10
b
bCos
bCos
36.9
4814
1448
A nautical problem
The extension helps us find the hypotenuse.
We have a few angles and the distance to add.
42
42)3(14
14
48b
4.10
b
bCos
bCos
36.9
4814
1448
A nautical problem
The extension helps us find the hypotenuse.
We have a few angles and thedistance to add.
42
42
14
48
4.10
36.9
36.5136.942
4.524.1036.51 22
Harmonic Motion (Doing the Wave)
Way of writing the Sine function or Cosine function with time.
d = a Sin wtor d = a Cos wt
d is the distance from the origin or Equilibrium
a is for amplitude; w is like b in the normal function (changes period)
Period = Frequency = w
22w
Homework
Page 338 – 342# 3, 11, 16, 21,
26, 31, 36, 41, 47, 53
Homework Page 338 – 342# 9, 14, 19, 24,
27, 33, 40, 43, 52, 55