Transcript Objective- To solve problems involving the Pythagorean Theorem.

Do Now:
• A golf ball is launched at 20 m/s at an angle of
38˚ to the horizontal.
1. What is the vertical component of the velocity?
2. What is the horizontal component of the
velocity?
3. What does the word “component” mean to
you?
Objective- To solve problems involving the
Pythagorean Theorem and Trig Identities
For Right Triangles Only!
leg
hypotenuse - always opposite
the right angle
leg
Objective- To solve problems involving
the Pythagorean Theorem.
For Right Triangles Only!
hypotenuse
leg a
c
b
leg
Objective- To solve problems involving
the Pythagorean Theorem.
For Right Triangles Only!
hypotenuse
ba
c
ba
Objective- To solve problems involving
the Pythagorean Theorem.
For Right Triangles Only!
Pythagorean Theorem
a
c
b
a b c
2
2
2
Solve for x.
a b c
2
6
x
8
2
2
6 8  x
2
36  64  x
2
100  x
2
2
2
100  x
10  x
2
x  10 or 10
Solve for y.
a b c
2
2
2
7 4  y
2
49  16  y
2
65  y
2
7
4
y
2
2
65  y
2
65  y
y  65 or  65
y  8.1
Solve for t.
6
a b c
2
15
2
t  6  15
2
t  36  225
36  36
2
t
2
2
2
t  189
2
t  189
t  189
t  13.7
2
Pythagorean Triples
3
4
5
6
8
10
9
12
15
12 16
20
Pythagorean Triples
3
4
5
5
12
13
7
24
25
6
8
10
10
24
26
14
48
50
9
12
15
15
36
39
21
72
75
12 16
20
12
9
15
To the nearest tenth of a foot, find the length
of the diagonal of a rectangle with a width of
4 feet and a length of 10 feet.
a b c
2
2
2
2
4 ft.
x
10 ft.
2
4  10  x
2
16  100  x
2
116  x
2
116  x
2
x  116
x  10.8
A car drives 20 miles due east and then 45 miles
due south. To the nearest hundredth of a mile,
how far is the car from its starting point?
a b c
2
2
2
2
20 miles
x
45 miles
2
20  45  x
2
400  2025  x
2
2425  x
2
2425  x
2
x  2425
x  49.24
TRIGONOMETRIC
IDENTITIES
SohCahToa
OPP
SIN=
HYP
OPP
TAN=
ADJ
ADJ
COS=
HYP
OPP
SIN=
HYP
X
Soh
ADJ
COS=
HYP
X
Cah
OPP
TAN=
ADJ
X
Toa
SAMPLE RIGHT TRIANGLE PROBLEMS
1.)
x
20
A
B
z
30
Ø
C
y
Find the values to the nearest tenth of:
B/A
A.) sin Ø = _______
A.) XY = ________
11.5
C/A
B.) cos Ø = _______
23.1
B.) YZ = ________
B/C
C.) tan Ø = _______
60
A ship sails 340 kilometers on a bearing of 75
degrees.
A. How far north of its original position is the ship?
B. How far east of its original position is the ship?
B
A. Cos 75 = A
340
B. Sin 75 =
B
340
A
340
75