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Try Now: In 2005, the Pythagorean Theorem was a deciding factor in a case before the New York
State Court of Appeals. A man named Robbins was convicted of selling drugs within 1000 feet of a
school. In the appeal, his lawyers argued that Robbins wasn’t actually within the required distance
when caught and so should not get the stiffer penalty that school proximity calls for.
The arrest occurred on the corner of Eighth Avenue and 40th Street in Manhattan. The nearest
school, Holy Cross, is on 43rd Street between Eighth and Ninth Avenues. The distance up Eighth
Avenue is 764 feet and the distance to the church along 43rd Street is 490 feet.

What’s the distance that a person would have to walk to get from Holy Cross to where
Robbins was arrested?

What’s the straight line distance from Holy Cross to where he was arrested?

How much farther is it to walk from the arrest site to Holy Cross as opposed to ‘as the crow
flies’?
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In the movie, “The Wizard of Oz”, Dorothy is swept away to a magical land in a tornado and embarks upon a quest to
see the Wizard who can help her return home. Accompanying her on this journey are a scarecrow (looking for brains),
a tin man (looking for a heart), and a lion (looking for courage).
When the wizard bestows an honorary degree of “thinkology” upon the scarecrow, the scarecrow recites
Pythagorean’s Theorem:
"The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the
remaining side."
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1
A right triangle has legs of lengths
𝑎 = 3 𝑚, 𝑏 = 10 𝑚. Find the unknown length of
the hypotenuse. Round your answer to the
nearest tenth.
Answer:
3
2
Answer:
Answer:
m
James wants to draw a line diagonally across a
rectangular piece of paper. If the paper
measures 9 inches by 12 inches, what is the
minimum length of the straight-edge he needs
to make the line?
inches
A telephone worker needs to run a guide wire
from the top of a 40-foot telephone pole to the
ground. He measures the distance from the
base of the pole to the point of the ground
where the wire would end to be 30 feet. Find
the length of wire that the worker will need.
4
feet
If a pool table measures 4 ft by 8 ft, what is the
diagonal length from the back edge of the top
left pocket to the bottom right pocket in
simplest radical form?
Answer:
feet
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5
The course for a local triathlon has the shape of a
right triangle. The legs of the triangle consist of a 4
mile swim and a 10-mile run. The hypotenuse of
the triangle is the biking portion of the event. How
far is the biking part of the triathlon? Round your
answer to the nearest tenth if necessary. Show
your work.
Answer:
7
miles
The bottom of a ladder is placed 4 feet from
the side of a building. The top of the ladder
must be 13 feet off the ground. What is the
shortest ladder that will do the job?
Answer:
6
Answer:
8
feet
A community is building a square park with sides
that measure 110 meters. To separate the picnic
area from the play area, the park is split by a
diagonal line from opposite corners. Determine
the approximate length of the diagonal line that
splits the square. Round your answer to the
nearest tenth.
meters
You and a friend stand back-to-back. You run 20
feet forward, then 15 feet to your right. At the
same time, your friend runs 16 feet forward, then
12 feet to her right. She stops and hits you with a
snowball!
How far does your friend throw the snowball?
Answer:
feet
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9
If you know that the two sides of a right triangle
measure 10 in. and 8 in., why is this not
enough information to be sure of finding the
length of the third side?
10
Clifford’s dog house is shaped like a tent. The
slanted sides are both 5 feet long and the bottom
of the house is 6 feet across. What is the height
of his dog house, in feet, at its tallest point?
Answer:
feet
Page 6 of 6
11
A store advertises the size of television
screens using the diagonal measurements
of the screens.
Part A: A television is advertised as having a
45 inch screen. If the screen is 36 inches wide,
what is the area of the screen in square
inches?
Answer:
square inches
Part B: A wide-screen television is advertised as having a
48 inch screen. The height of the screen is 24 inches. Is
the width of the screen actually 48 inches? Explain your
answer.