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Geometry – Unit 6 Practice
Pythagorean Theorem - Application
Name: _____________________________!
Date: ___________ Pd: ____
G.SRT.C.8
1. Tommy Turtle wanders off in the zoo. Hilda Hippo saw him walk to the “T” on 1st Street and make a
right. The T is 1.2 miles from Tommy’s pen. Gertrude Giraffe can see Tommy sitting outside the giraffe
area. The giraffe area is 1.6 miles from the “T”. Exactly how far is Tommy Turtle from his pen?
2. Gino is terrified of heights above 9 feet. He is asked to repair a high wall. The bottom of a ladder must
be placed 6 feet from the wall. The ladder is 10 feet long. How far above the ground does the ladder
touch the wall? Will Gino be able to do the repair?
3. A helicopter rose vertically 300 m and then flew west 400 m. How far was the helicopter from its
starting point?
4. James leaves his house to walk to school. He walks 200 m west and 125 m north. Calculate how far he is
from his house.
5. Television screen sizes are determined by the length of the diagonal portion of the screen, rounded to
the nearest whole number. A television screen has a 20 inch width and the height measures 16 inches.
Calculate the screen size.
6. City A is 14 miles from city B, and 7 miles from city C. Cities A, B and C form a right triangle at A. A road
connects cities B and C directly. What is the length of this road?
7. After driving north for hours, Julie finds the highway blocked by a herd of buffalo. Her choice is to wait
for them to clear or to drive around them. The dirt road detour takes her 6 miles east then turns
heading northwest and meets the highway 8 miles north of her current position. The detour road has a
maximum speed of 20 mph. If the buffalo take 20 minutes to clear, assuming she can drive 60 mph on
the highway, how much time can she save by waiting?
8. John bought a 6-ft-square sheet of plywood to build a display case for his math trophies. Will the
plywood fit in the back of his van? The opening of the van is 44 inches high and 60 inches wide. Justify
your answer.
9. A science class is doing an experiment using pulleys to raise a
pole. Some students say that the pole will stand at a right angle
to the ground when the length of the rope between the pulley
and the top of the pole is 17 ft. Were they correct in saying the
pole would be at right angles with the ground?
10. The Smith's are installing a wide-screen television with a 60-inch diagonal. Their entertainment center is
46 inches wide by 36 inches high, will the television fit in their current entertainment center? Justify
your answer.
11. Math often shows up in sports in ways that we don’t realize. Take for example the softball diamond. It is
actually a square with the bases set at 90° angles. If the bases are 60 feet apart, how far is it from home
plate to second base? Round to the nearest tenth.
SNRPDP
Unit 6: Right Triangles & Trigonometry
NVACS – Revised 2014-2015
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Practice – Unit 6 (cont.)
12. A park is in the shape of a rectangle 8 miles long and 6 miles wide. How much shorter is your walk if you
walk diagonally across the park than along two sides of it?
13. A tent is supported by a guy wire tied to a stake, as shown in the
diagram. What is the length of the rope?
14. The diagram at the right shows how a post was broken. What was the original height of
the post?
15. A lifeguard spots a drowning swimmer 40 ft. from the beach.
She runs 90 ft. along the beach at a speed of 15 feet per second,
then jumps in the water and swims straight to the swimmer at a
speed of 5 feet per second. How long does it take her to reach
to swimmer?
16. Mrs. Robinson always decorates her rectangular window with lights. She has the
lights to go around the edge of the window as shown but wants to add lights on the
diagonals. How many more feet of lights will she need? The lights are sold in 10 foot
spans, how many sets will she need to purchase?
5
ft
8 ft
17. Two trains left Metropolis at the same time. One traveled south at 50 mph. The other traveled east at 40 mph.
How far apart were the trains at the end of 3 hours?
18. A newly-planted tree needs to be staked with three wires. Each wire is attached to the
trunk 3 ft. above the ground, and then anchored to the ground 4 ft. from the base of the
tree. How much wire is needed for 6 trees?
19. A 30 foot waterslide extends 18 feet out into the water. How high is the top of the slide?
20. A quarterback at point A throws the football to a receiver who catches it at point B.
How long was the pass?
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