Some Applications of Pythagorean Theorem
(which should really make you think!)
For each of the following problems, draw a diagram, clearly labelling the right-triangle(s) which
you are using in your solution, and solve the problem.
1. A baseball diamond is actually a square (rotated a little!). 1st base is 90 feet from home, and 2nd
base is 90 feet from 1st, etc. When someone tries to steal 2nd base, how far does the catcher need
to throw the ball from home in order to reach 2nd base?
2. A 7.8 m long ladder is leaning up against a wall. If the ladder is 2.2 m away from the wall at the
base, how far up the wall does the ladder reach?
3. Suppose you leave home and drive 14 km west then 8 km north. How far are you from home
"as the crow flies" (straight line from starting point to end point)?
4. What is the longest straight-line distance between any two vertices of a cube (to 1 decimal), if
the cube has a volume of 551.368 cm3?
5. You and your friend are standing on one corner of a rectangular field. The field is 85 m wide,
and 112 m long. If you can walk 3 m/s, and walk around the outside of the field to the farthest
corner, and your friend walks 2 m/s but walks straight across the diagonal of the field to the
farthest corner, who arrives first?
6. Mr. Foster is 182 cm tall. If he is standing 2.5 m away from a flower that is 46 cm tall, how far is
it from the top of his head to the top of the flower?
7. What is the area of the shaded region in the figure below?
18 cm
8 cm
10 cm
8. You are standing at a window 4.8 m above the ground, and are holding a piece of rope that is
22.7 m long, with a tent peg tied to the end. If you have another friend pull the rope away from
the building until it is as tight as possible, and peg it into the ground, how far away from the base
of the building is the tent peg?
9. Consider question 2 again. If the wall was only 6.6 m high, and the ladder was rested on the top
corner of the wall, and was still 2.2m away at the base, how high straight above the top of the wall
would the ladder reach?
Answers (all rounded):
1.
2.
3.
4.
5.
6.
7.
8.
9.
127.3 ft
7.5 m
16.1 km
14.2 cm
You do (65.7 s vs. 70.3 s)
284.6
40.5 cm2
22.2 m
0.8 m