4. Pythagoras Theorem: In a right triangle, the area of the
square on the hypotenuse is equal to the sum of the areas
of the squares of its remaining two sides.
(Hypotenuse)2=(Perpendicular)2+(Base)2
(AC)2=(CB)2+(BA)2
For Pythagorean triplets:
a2+b2=c2
a=6
b=8
c=10
∴62+82=36+64=100=102
That is a2+b2=c2
Hence 6,8,10 are Pythagorean triplets.
42. Check It Out! Example 2
A rectangular field has a length of 100 yards and a
width of 33 yards. About how far is it from one corner
of the field to the opposite corner of the field? Round
your answer to the nearest tenth.
43. Check It Out! Example 2 Continued
1 Understand the Problem
Rewrite the question as a statement.
• Find the distance from one corner of the field to the
opposite corner of the field.
• The segment between the two corners is
the hypotenuse.
• The sides of the fields are legs, and they are 33 yards long
and 100 yards long.
List the important information:
• Drawing a segment from one corner of the field to the
opposite corner of the field divides the field into two
right triangles.
44. Check It Out! Example 2 Continued
2 Make a Plan
You can use the Pythagorean Theorem to
write an equation.
45. Check It Out! Example 2 Continued
Solve
3
a2 + b2 = c2
332 + 1002 = c2
1089 + 10,000 = c2
11,089 = c2
105.304 c
The distance from one corner of the field to the
opposite corner is about 105.3 yards.
Use the Pythagorean Theorem.
Substitute for the known variables.
Evaluate the powers.
Add.
Take the square roots of both sides.
105.3 c Round.
46. The Pythagorean Theorem
“For any right triangle,
the sum of the areas of
the two small squares is
equal to the area of the
larger.”
a2 + b2 = c2
47. "The area of the square built
upon the hypotenuse of a right
triangle is equal to the sum of the
areas of the squares upon the
remaining sides."
50. Baseball Problem
A baseball “diamond” is really a square.
You can use the Pythagorean theorem to find
distances around a baseball diamond.
51. Baseball Problem
The distance between
consecutive bases is 90
feet. How far does a
catcher have to throw
the ball from home
plate to second base?
52. Baseball Problem
To use the Pythagorean
theorem to solve for x,
find the right angle.
Which side is the
hypotenuse?
Which sides are the legs?
Now use: a2 + b2 = c2
53. Baseball Problem
Solution
• The hypotenuse is the
distance from home to
second, or side x in the
picture.
• The legs are from home to
first and from first to
second.
• Solution:
x2 = 902 + 902 = 16,200
x = 127.28 ft
54. Ladder Problem
A ladder leans against a
second-story window of a
house.
If the ladder is 25 meters
long,
and the base of the ladder
is 7 meters from the
house,
how high is the window?
55. Ladder Problem
Solution
• First draw a diagram that
shows the sides of the
right triangle.
• Label the sides:
– Ladder is 25 m
– Distance from house is 7
m
• Use a2 + b2 = c2 to solve
for the missing side.
Distance from house: 7 meters