Download The Pythagorean Theorem: a + b = c

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
Name
Alg 1
Right Triangle
Mr. McCormack
5
Q4 Quiz 6 Review
1)
2)
x
x
222
125
35
6x
15
3)
4)
7
x
42
31
5)
6)
21
9
x
When printing off the school website, all the info on angles will be missing.
Name
Alg 1
7)
Right Triangle
Mr. McCormack
x
8)
14
9)
x
10)
x
x+8
32
x+5
2x + 9
2x + 8
x+7
When printing off the school website, all the info on angles will be missing.
6
Name
Alg 1
Right Triangle
Mr. McCormack
7
Right Triangle Word Problems  DRAW A PICTURE!!!
1) 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?
2) 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)?
3) The dimensions of a rectangle are 12m and 4m. Find the length of the diagonal to the nearest
tenth.
When printing off the school website, all the info on angles will be missing.
Name
Alg 1
Right Triangle
Mr. McCormack
4) A boy is sitting on the floor flying a kite. He has 260 feet of string. If the kite is 195 feet
high, find the angle of elevation.
5) A ladder is leaning against a building. If the angle of depression is 58º and the base of the
ladder is 9 feet from the base of the building? How long is the ladder?
6) A boy is sitting on the floor flying a kite. He has 450 feet of string. The angle of elevation is
64°. How high is the kite?
When printing off the school website, all the info on angles will be missing.
8
Name
Alg 1
Right Triangle
Mr. McCormack
7) An apple tree casts a 23-foot shadow. If the angle of depression is 36°, how tall is the tree?
8) A bird is perched on top of a 22-foot oak tree. It sees a piece of bread on the ground, 45 feet
from the base of the tree. How far will the bird have to fly to get the piece of bread?
9) A 15-foot ladder is leaning against a building. The base of the ladder is 4 feet away from the
base of the building. Find the angle of elevation created by the ladder.
When printing off the school website, all the info on angles will be missing.
9
Name
Alg 1
Right Triangle
Mr. McCormack
10
10) An eagle flies 16 miles north and then 12 miles west. How far is the bird from the staring
point?
11) A statue casts a 62-foot shadow. If the height of the statue is 45 feet, find the angle of
depression.
12) A slide is attached to the side of a tree house. The height of the tree house is 10 feet more than
the double the distance from the base of the tree to the base of the slide. The length of the slide is 1
more than the height of the tree house. Find the length of the slide.
When printing off the school website, all the info on angles will be missing.
Name
Alg 1
Right Triangle
Mr. McCormack
11
Q4 Quiz 7 Review:
1) The area of a square is 64 in2. Find the perimeter.
2) The perimeter of a square is 144 cm. Find the area.
3) The area of a square is 49 cm2. Find the length of the square’s diagonal to the nearest tenth of a
cm.
4) Dora the Explorer is pelting Spongebob with rocks from a 6th story fire escape. If Spongebob is
35 feet from the base of the building and the angle of depression is 63º, what distance (to the nearest
tenth of a foot) is the rock traveling?
5) Hojas is back and he is sitting on the floor flying a kite. He has 410 feet of string. If the kite is
361 feet high, find the angle of elevation to the nearest tenth of a degree.
6) A statue of Stembridge casts a 42-foot shadow. If the angle of depression is 61°, how tall is the
statue, to the nearest hundredth of a foot?
7) An eagle flies 10 miles north and then 6 miles west. How far is the bird from the staring point?
Round your answer to the nearest thousandth.
8) The dimensions of a rectangular sandbox are stated in feet as the width being x + 9 and the length
being x + 16. If the rectangle’s diagonal is x + 17, find the perimeter of the garden.
9) A slide is attached to the side of a tree house. The height of the tree house is 6 less than double
the distance from the base of the tree to the base of the slide. The length of the slide is 3 more than
the height of the tree house. Find the length of the slide.
10) The area of a rectangle is 50 yds2. The length is represented by x + 11. The width is
represented by x + 6. Find the length of the rectangle’s diagonal in simplest radical form.
Answer Key:
1) 32in
2) 1,296 cm2 3) 9.90 cm
4) 77.1 ft
5) 61.7º
6) 75.77 ft
7) 11.662 miles
8) x = -4; sides = 5,12,13; p = 30ft
9) 15 feet
10) x = -1; w=5; l=10; diagonal = 11.18 yards
When printing off the school website, all the info on angles will be missing.