Name
Alg 1
Right Triangle
Mr. McCormack
The Pythagorean Theorem:
a2 + b2 = c2
For all right triangles:
a= 3
b= 4
(where c is the hypotenuse)
c= ?
Pythagorean Triples
3,4,5
5,12,13
7,24,25
8,15,17
9, 40, 41
c
32 + 42 = c2
9 + 16 = c2
25
= c2
25 =  c2
5
=c
3
4
Right Triangle Trigonometry: SOH-CAH-TOA
SOH:
sin = opposite
hypotenuse
B
CAH: cos = adjacent
hypotenuse
TOA: tan = opposite
adjacent
B
hypotenuse
adjacent
hypotenuse
opposite
A
C
opposite
Based on angle B
A
C
adjacent
Based on angle C
The hypotenuse is always the side opposite the right angle. The opposite and adjacent depend on
which angle you are looking at.
opposite: The side directly across from the angle (does not touch the angle).
adjacent: (Next to) The side that touches the angle, but is not the hypotenuse.
When deciding when to use the Pythagorean Theorem or Trigonometry, the rule of thumb is that if
there is an angle involved in the problem, use the trigonometry. If you are dealing only with
missing sides (no angles), use the Pythagorean Theorem.
When printing off the school website, all the info on angles will be missing.
1
Name
Alg 1
Right Triangle
Mr. McCormack
Use the Pythagorean Theorem to solve for the missing side:
1)
2)
3)
x
x
11
x
39
36
18
x
17
Use the SIN to find the missing side:
4)
5)
9
x
x
15
When printing off the school website, all the info on angles will be missing.
2
Name
Alg 1
Right Triangle
Mr. McCormack
Use the COS to find the missing side:
6)
x
7)
21
x
14
Use the TAN to find the missing side:
8)
11
9)
x
x
13
Use SIN, COS, and TAN to find the missing angle:
10)
11)
18
9
12)
14
13
13
17
When printing off the school website, all the info on angles will be missing.
3
Name
Alg 1
Right Triangle
Mr. McCormack
Mixed Problems: Find x (You will have to choose whether to use Pythagorean Theorem or trig.).
Round all sides to the nearest tenth and all angles to the nearest degree:
1)
2)
x
3)
x
10
15
14
24
x
4)
5)
10
6)
x
11
x
16
23
7)
31
8)
9)
12
x
10
19
37
7
10)
x
11)
12)
17
20
x
x
When printing off the school website, all the info on angles will be missing.
x
18
4