Before Class Work

1
Before Class Work
Name
TG
1/30/06
Two runners leave the city of Watertown at noon.
One runner travels north and the other travels
east. Suppose the northbound runner is running 6
miles per hour and the eastbound runner is
running 5 miles per hour. Make a table that
shows the distance each runner has traveled and
the distance between the two runners after 1
hour, 2 hours, and 3 hours.
6 mph
5 mph
Watertown
Hours Distance traveled by northbound runner (miles) Distance traveled by eastbound runner (miles) Distance apart (miles)
1
2
3
2
Looking For Pythagoras

• Investigation 4.3
• Finding the Perimeter

3
Problem 4.3 In the diagram below, some lengths
and measures are given. Use this info and what
you have learned in this unit to help you find
the perimeter of triangle ABC. Explain your work.
C
30
A
B
D
8
4
Problem 4.3 Follow-Up Find the area of triangle
ABC. Explain your reasoning.
C
30
A
B
D
8
5
Problem 4.3 Follow-Up Find the areas of triangles
ACD and triangle BCD. Explain your reasoning.
C
30
A
B
D
8
6
30-60-90 Right Triangle
The leg opposite the 30 degree angle is always ½
of the length of the hypotenuse.
30
6
60
3
7
45-45-90 Right Triangle
A
B
The triangles are congruent.
45
45
In a 45-45-90 right triangle, two sides are
equivalent.
45
45
C
D
8
Problem 4.3 In the diagram below, some lengths
and measures are given. Use this info and what
you have learned in this unit to help you find
the perimeter of triangle ABC. Explain your work.
C
60
30
30
60
A
B
D
8
9
Problem 4.3
The leg opposite the 30 degree angle is always ½
of the length of the hypotenuse.
C
16
60
30
30
60
A
B
D
8
10
Problem 4.3
The leg opposite the 30 degree angle is always ½
of the length of the hypotenuse.
C
16
30
60
A
B
32
11
Problem 4.3
Use the Pythagorean Theorem.
C
Is this length 768?
16 x 16 256
16
32 x 32 1,024
1,024 256 768
30
60
A
B
32
768 27.7
12
Problem 4.3
Find the area of ABC.
C
What two numbers do we use for area?
27.7
16
30
60
A
B
32
13
Problem 4.3
Find the area of ABC.
C
What two numbers do we use for area?
27.7
16
16 x 27.7 443.2
30
60
A
B
32
Cut 443.2 in half 221.6
14
Problem 4.3 Follow-Up Find the areas of triangles
ACD and triangle BCD. Explain your reasoning.
C
16
27.7
30
A
B
D
8
32
15
Problem 4.3 Follow-Up Find the areas of triangles
ACD and triangle BCD. Explain your reasoning.
C
16
27.7
30
A
B
D
8
24
32
16
Problem 4.3 Follow-Up
Area of triangle ACD.
C
Find CD first.
16
27.7
16 x 16 256
192
8 x 8 64
256 64 192
30
A
B
D
8
24
192 13.9
32
17
Problem 4.3 Follow-Up
Area of triangle ACD.
C
8 x 13.9 111.2
16
27.7
Cut 111.2 in half
13.9
½ of 111.2 55.6
30
Area of ACD 55.6
A
B
D
8
24
32
18
Problem 4.3 Follow-Up
Area of triangle BCD.
C
24 x 13.9 333.6
16
27.7
Cut 333.6 in half
13.9
½ of 333.6 166.8
30
Area of ACD 166.8
A
B
D
8
24
32
19
HW Problem 2, Page 47
15 m
15 m
45
45
1000 m
How long, to the nearest tenth of a meter, is the
cable for the Sky Breaker ride?
20
HW Problem 3, Page 47
2 feet
What is the tallest tree that can be braced with
a 25-foot wire staked 15 feet from the base of
the tree?
25 feet
15 feet
21
HW Problem 4, Page 48
How tall is the Beaumont Tower? Explain how you
found your answer.
60
5 feet
58 feet
22
Show your work here