## Monday, November 15, 2010

### Finding Side Lengths

A baseball diamond is a square. How could you determine the distance
from second base to home plate? How many different strategies can
you develop?Determine the length of leg s of the
right triangle

a2+ b2= c2
(27x27) + (27x27) = c2
729m(squared) + 729m(squared)
c21458= c2
1158cm(squared
c238.18m= c

• The Pythagorean relationship can be used to determine the length of the hypotenuse of a right triangle when the lengths of the two legs are known.

a2+b2=c2
3cm+4cm=c2
3x3=9
4x4=16
9+16=25cm
25 square root=5
c=5

• The Pythagorean relationship can be used to determine the leg length of a right triangle when the lengths of the hypotenuse and the other leg are known.

p2 + q2 = r2
p2 + 122 = 152
p2 + 144 = 225
p2 + 144 - 144 = 225 - 144
p2 = 81
p = √
___
81
p = 9

1. Jack must determine the missing side length of a triangle. He decides to draw it and then measure it, as shown. Do you agree with the method that Jack is using? Explain

I do not agree because, one it would take to long, two when I drew a triangle on grid paper it was very hard to measure the hypotenuse, also its just a lot quicker to use Pythagorean relationships.

2.Kira calculated the missing side length of the right triangle.
y2 = 52+132
y2 = 25
169y2 = 194y2
≈ 13.9
The length of side y is approximately 13.9 cm. Is Kira correct? If she is correct, explain how you know. If she is incorrect,explain the correct method.

Kira is correct because 5x5=25 and 13x13=16
169+25=194
194 square root= 13.9

3. Determine the length of each hypotenuse.

a)
a2+b2=c2
a=12cm 12cm+16cm=c2
b=16cm 12x12=144cm
20cm 16x16=256
144+256=400
400 squared=20

b)
c2-a2=b2
a=16m 30m-16m-c2
b=25.3m 30x30=900
c=30m 16x16=256
900-256=644
644 square root=25.3

4. What is the length of each hypotenuse?
a centimetre.
a)
a=6cm a2+b2=c2
b=7cm 6cm+7cm=c2
c=9.2cm 6x6=36
7x7=49
36+49=85
85 square rooted=9.2

b)
c2-b2=a2
a=7.5cm 11cm-8cm=a2
b=8cm 11x11=121
c=11cm 8x8=64
121-64=57
57 square rooted=7.5