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.
1
Name
Alg 1
Right Triangle
Mr. McCormack
Find X to the nearest tenth:
1)
13
2)
14
X
X
11
Find missing side to the nearest hundredth:
3)
4)
X
17
13
X
Find the missing side in simplest radical form:
5)
6)
X
9
5
18
X
10
Find the missing angle:
7)
8)
14
11
15
22
2
Name
Alg 1
Right Triangle
Mr. McCormack
1) tenth
2) simplest radical form
x
9
3
3) hundredth
24
12
x
5
21
x
4) A 25-foot ladder is leaning against a building. The base of the ladder is 7 feet away from the
base of the building. How far up the building is the top of the ladder resting?
5) A bird is perched in a tree. It is 35 feet off the ground. It sees a piece of bread on the ground
15 feet from the base of the tree. How far will the bird have to fly to get the bread (round to the
nearest hundredth)?
6) The dimensions of a rectangle are 12m and 4m. Find the length of the diagonal to the nearest
tenth.
7) The area of a rectangle is 72 ft2. The length is represented by x + 1. The width is represented
by x – 5. Find the length of the rectangle’s diagonal to the nearest tenth of a foot.