NAME: ______PERIOD: ______
WS 9.3 B - CONVERSE OF P.T.
1) What’s wrong with this picture?
2) Lou and his family went sailing at South Padre Island. The shape of their sail is a right triangle. If the height of the sail is 20 ft and its hypotenuse is 23 ft, which expression could you use to calculate the length of the third side of the sail?
A) C)
B) D)
3) This diagram represents the sign at a museum in Houston. If the base of the sign is 18 ft and
the hypotenuse of each right triangle is
10.5 ft, which expression gives the
altitude, or height, of the sign?
A) C)
B) D)
4) A maypole was cemented into the ground at a park. The top of the pole is 15 ft above the ground.
A child stands 5 ft from the pole and reaches
upso her hand is 4 ft above the ground.
What isthe distance from the child’s hand
to the topof the pole?
A) 6.4 ftC) 15.5 ft
B) 12.1 ftD) 15.8 ft
5) The lengths of the legs of a right triangle are 5 and 7. Which expression can you use to find the length of the third side of the triangle?
A) C)
B) D)
6) A pole has two guy wires supporting it. One wire is 20 ft long and attaches to the pole 15 ft above the ground. The other wire is 19 ft long and attaches to the pole 14 ft above the ground. Which wire is anchored to the ground closer to the base of the pole?
A) the 20-ft wire
B) the 19-ft wire
C) they are anchored the same distance from the base
D) it will depend on the angle they form w/ the ground
7) The side of a TV screen refers to the length of a diagonal of the screen. If a screen size is
advertised as 27 inches and its length is
21 inches, what is its height?
A) 17.0 in.C) 34.0 in
B) 19.1 inD) 36.4 in
8) A set of swings is built so the two vertical supports are at opposite corners of a rectangle that is 20 ft by 35 ft. How long is the pole that joins the
two vertical supports?
A) 7.4 ftC) 35 ft
B) 28.7 ftD) 40.3 ft
9) When window blinds are made, the cord is attached so it forms a diagonal of the window. How
much cord is used for the diagonal if the
length of the window is 24 in. and its
height is 36 in.?
A) 26.8 inC) 52.1 in
B) 43.3 inD) 60.0 in
10) A 50-foot clothesline is hung along the diagonal of a rectangular yard. If the length of the yard is 30 feet, how many feet are in the width of the yard?
______
11) A surveyor wanted to know the height of a totem pole on an Indian reservation. Using the measure- ments in the diagram, what is the height of the totem pole?
A) 10.5 m
B) 7.5 m
C) 4.3 m
D) 1.5 m
12) A brace is placed diagonally across
the back of a bookshelf. How long is
the brace if the length of the bookshelf
is 3 ft, the height is 5 ft, and the book-
shelf is 1.5 ft deep?
A) 5.8 ftC) 4.7 ft
B) 5.2 ftD) 3.4 ft
13) Don is helping his father paint a house. He sets a 12-foot ladder against the house so the base of the ladder is 5 feet from the house. How far up the house does the ladder reach?
A) 17.1 ft
B) 13.0 ft
C) 10.9 ft
D) 7.1 ft
14) Diane left her home in El Paso and walked 2 km north, 6 km west, 5 km north, and 1 km west to get to her friend Gail’s house. What is the straight-line distance between the two homes?
A) 5.8 kmC) 9.9 km
B) 8.6 kmD) 14 km
15) A 15-ft ladder leaning against a house reaches a point 14 ft from the ground. Which expression can you use to find the distance between the foot of the ladder and the house?
A) C)
B) D)
16) This diagram shows one of the guy wires that secure a telephone pole to the ground. Which two variables represent the lengths of the legs of a right triangle?
A) and
B) and
C) and
D) The triangle is not a right triangle.
17) A baseball field is a square and each side of the square is 90 feet. During a double play, the ball is thrown from third base to first base. Which term can represent the path of the thrown ball?
A) heightC) hypotenuse
B) medianD) leg
18) One leg of a right triangle is units long, the other leg is 2 units longer than the first leg, and the hypotenuse is 10 units long. How long is thefirst leg?
(Since you have the answers, use each
one to “guess & check” until you find
the one that works!!)
A) 8 units
B) 6 units
C) 2 units
D) 1 unit
19) A cell transmission tower is 100 ft high. A guy wire connects a point halfway up the tower to a point on the ground 30 ft from its base. How many feet long is the guy wire?
______
20) Two vertices of a right triangle are and . Which are possible coordinates of ?
A)
B)
C)
D)
21) Which are the lengths of the sides of a right triangle?
A) 3 ft, 4 ft, 6 ft
B) 6 mm, 9 mm, 12 mm
C) 5 cm, 12 cm, 14 cm
D) 16 m, 30 m, 34 m
22) What is the radius of thiscircle?
A)
B)
C)
D)
E)
23) Two sides of a triangle have lengths 14 and 15 cm. How do you know that the length of the third side cannot be 30 cm?
A) 14 + 15 < 30C) 15 + 30 > 14
B) 14 + 30 > 15D) 142 + 152 302
23)
24) According to the map, the gas station is 5 km west and 2 km south of your house. The post office is 3 km east and 4 km north of your house. How many kilometers apart are the gas station and the post office?
______
25) Triangle is a right triangle with sides of length 4, 6, and . If , what is the approximate value of ?
A) 4
B) 4.47
C) 5.21
D) 5.63
E) 7.21
26)
27)