Download STAR CITY Math / Geometry / Special Right Triangles Name

STAR CITY
Math / Geometry / Special Right Triangles
Name _________________________________
Teacher ____________________ Period _____
2.
Use the diagram below to answer question 1.
1.
Lisa wants to lay a path of bricks from her
house to her gazebo. She needs to find the
distance from her house to the gazebo to
determine how many bricks to buy. What is
the distance of the diagonal from the house to
the gazebo? Round to the nearest tenth.
(Assume the area shown above is a square).
A.
40.0 ft.
B.
56.6 ft.
C.
69.3 ft
D.
80.0 ft.
The drawing shows the measurements in a
section of a circular design. How long is the
radius of the circle?
A.
10 cm
B.
8.7 cm
C.
7 cm
D.
4.3 cm
Use the figure below to answer question 3.
3.
1
What is the value of x?
A.
17 cm
B.
17 2 cm
C.
17 3 cm
D.
34 cm
STAR CITY – Math – Geometry – Special Right Triangles
4.
Use the diagram below to answer question 5.
Firemen are using a 75 ft. ladder extended to
70 ft. The ladder is positioned at a 60° angle
with the horizontal of the truck. How many
vertical feet is it from the top of the fire truck
to the tip of the ladder?
5.
A.
35 2 ft.
B.
35 3 ft.
C.
140 3
3
D.
ft.
35 ft.
6.
2
To get from point A to point B, Kevin must
avoid walking through a pond. To avoid the
pond, he has to walk 33 meters west and 65
meters southeast. How many meters would be
saved if he were to walk through the pond?
A.
25 m
B.
42 m
C.
56 m
D.
98 m
The hypotenuse of a 30°-60°-90° triangle
measures 10 inches. What is the area of the
triangle, rounded to the nearest hundredth?
A.
12.50 in.2
B.
17.68 in.2
C.
21.65 in.2
D.
25.00 in.2
STAR CITY – Math – Geometry – Special Right Triangles
7.
The diagram below shows some dimensions of
Comiskey Baseball Park in Chicago, Illinois.
¯
A is home plate, C is dead center field, and DB
is the segment from the left field foul-ball pole
to the right field foul-ball pole. If the center
fielder is standing at E, how far is he from
home plate?
Use the diagram below to answer question 9.
9.
8.
A.
131.7 ft.
B.
173.5 ft.
C.
245.4 ft.
D.
490.6 ft.
Find the value of x and y.
Susan and Jerilyn are standing at opposite
corners of a square field. Susan wants to throw
a ball to Jerilyn. How far does she have to
throw it? Round to the nearest tenth.
A.
40.0 ft.
B.
56.6 ft.
C.
69.3 ft.
D.
80.0 ft.
Use the figure below to answer question 10.
10. What is the approximate area of the sign if
each side is 36 inches long?
A.
x = 6 and y = 2 3
B.
x = 4 3 and y = 12
C.
x = 4 3 and y = 6
D.
x=
3 and y = 2 9
3
A.
108 in.2
B.
561 in.2
C.
648 in.2
D.
1,296 in.2
STAR CITY – Math – Geometry – Special Right Triangles
11. The perimeter of the square below is 36. What
is the length of the diagonal, x?
A.
6
B.
9
C.
6 2
D.
9 2
Use the figure below to answer question 13.
13. The Sailing Club participates in different
races. One race course is in the design of an
isosceles right triangle as shown above. A
buoy is placed at each vertex of the course.
The course starts at buoy 1, continues around
buoy 2, then buoy 3, and then returns to buoy
1. If the length of the course from buoy 1 to
buoy 2 is 3.5 nautical miles, what is the
approximate distance from buoy 3 to buoy 1?
12. The diagonal crossbar of an old wooden gate
has rotted. The gate is rectangular, 5 feet by 7
feet. About how long is the crossbar?
A.
4.9 feet
B.
8.6 feet
C.
9.9 feet
D.
12.0 feet
4
A.
1.87 nm
B.
2.47 nm
C.
3.06 nm
D.
8.66 nm
STAR CITY – Math – Geometry – Special Right Triangles
14. The Parks and Recreation Association is
installing the playground equipment shown
below at Ames Park.
Find the distance from the base of the slide to
the post.
A.
12 2 feet
B.
12 3 feet
C.
24 feet
D.
42 feet
5
STAR CITY
Open-Response / Geometry / Special Right Triangles
Name _________________________________
Teacher ____________________ Period _____
GEOMETRY OPEN-RESPONSE ITEM A
A.
The Titanic left port on April 10, 1912. When leaving Queenstown, the power of the Titanic broke the
ropes of the docked S.S. New York and pulled it into it's wake. The two ships nearly collided.
1. If the ships had collided at their bows as diagramed below, what would have been the approximate
distance between the sterns of the ships? Round your answer to the nearest foot. Show or explain all of
your work.
2. On April 15, 1912 at 2:10 A.M., the Titanic tilted 45° as the bow was submerging. The stern rose out
of the water as shown below.
If 380 ft. of the Titanic was not submerged at this time, approximately how far above the water was the
stern of the Titanic? Round your answer to the nearest foot. Show or explain all of your work.
BE SURE TO LABEL YOUR RESPONSES 1 AND 2.
6
STAR CITY
Name _________________________________
Student Answer Document / Geometry / Special Right Triangles
Teacher ____________________ Period _____
A
7
GEOMETRY OPEN-RESPONSE ITEM A (T.2.G.4, T.2.G.5B)
A.
The Titanic left port on April 10, 1912. When leaving Queenstown, the power of the Titanic broke the ropes of the docked S.S.
New York and pulled it into it's wake. The two ships nearly collided.
1. If the ships had collided at their bows as diagramed below, what would have been the approximate distance between the
sterns of the ships? Round your answer to the nearest foot. Show or explain all of your work.
2. On April 15, 1912 at 2:10 A.M., the Titanic tilted 45° as the bow was submerging. The stern rose out of the water as shown
below.
If 380 ft. of the Titanic was not submerged at this time, approximately how far above the water was the stern of the Titanic?
Round your answer to the nearest foot. Show or explain all of your work.
BE SURE TO LABEL YOUR RESPONSES 1 AND 2.
RUBRIC FOR GEOMETRY OPEN-RESPONSE ITEM A (T.2.G.4, T.2.G.5B)
Score
Description
4
The student earns 4 points. The responses contain no incorrect work. The unit "feet" must be
included in Parts 1 and 2.
3
The student earns 3 points.
2
The student earns 2 points.
1
The student earns 1 point. Some minimal understanding is shown.
0
The student earns 0 points. No understanding is shown.
B
Blank. No response. No attempt to answer the item.
Solution and Scoring
Part 1: 2 points possible
1 point: Correct answer: 681 ft.
AND
1 point: Correct and complete procedures shown or explained.
Work may include a copy or calculation error, but not a procedural error.
8822 = 5602 + x 2
x 2 = 464324
x = 681.4 ≈ 681 ft.
The sterns of the ship would have been about 681 feet apart if the ships would have
collided at their bows.
Part 2: 2 points possible
1 point: Correct answer: 269 ft.
AND
1 point: Correct and complete procedures shown or explained.
Work may contain a calculation or copy error, but not a procedural error.
Give credit for the following or equivalent.
380 = 2 ⋅ x
sin 45o =
380
2
0.707 =
=x
x = 268.7 ≈ 269 ft.
OR
x
380
x
380
x = 268.7 ≈ 269 ft.
x 2 + x 2 = 3802
OR
2x 2 = 144,400
x 2 = 72,200
x = 268.7 ≈ 269 ft.
The stern of the Titanic would have been about 269 feet above the water at this time.
STAR CITY
Math / Geometry / Special Right Triangles
Answer Key and Alignment
Answer
1. B
2. A
3. B
4. B
5. B
6. C
7. C
8. C
9. B
10. B
11. D
12. B
13. B
14. B
Source
TLI
TLI
TLI
TLI
TLI
AR
TLI
TLI
AR
TLI
AR
TLI
TLI
AR
SLE
T.2.G.4
T.2.G.5a
T.2.G.5b
T.2.G.5a
T.2.G.4
T.2.G.5a
T.2.G.5b
T.2.G.4
T.2.G.5b
T.2.G.5a
T.2.G.5b
T.2.G.4
T.2.G.5b
T.2.G.5a