Deck 18: Triangles

Question 1

Find the value of y given that the two triangles, 6ABC and 6DEF, are similar.

A)38.5
B)21.6
C)12.6
D)53.4

Answer 1

D

Question 2

If the sides of a triangle measure 12 m, 12 m, and 1,200 cm, what kind of triangle is it?

A)isosceles triangle
B)right triangle
C)scalene triangle
D)equilateral triangle

Answer 2

D

Question 3

Find the value of x given that the two triangles, 6ABC and 6DEF, are similar.

A)12.6
B)21.6
C)38.5
D)7.3

Answer 3

A

Question 4

Find the height to the nearest foot of a tree that makes a 50-foot shadow when a 2 ft. 6 in. pole is used to make a shadow of 3 feet.

A)24 ft
B)95 ft
C)42 ft
D)25 ft

Question 5

What is the name of a triangle with three equal sides?

A)right triangle
B)isosceles triangle
C)equilateral triangle
D)scalene triangle

Question 6

If the sides of a triangle measure 15 m, 18 m, and 22 m, what kind of triangle is it?

A)right triangle
B)isosceles triangle
C)equilateral triangle
D)scalene triangle

Question 7

Identify the smallest angle in the given triangle

A)zA
B)zB
C)zC
D)insufficient information

Question 8

The given triangles are congruent with BC = EF. Write the corresponding part for zB from triangle DEF.

A)zE
B)zD
C)zF
D)zA

Question 9

What is the name of a triangle with no equal sides?

A)right triangle
B)scalene triangle
C)equilateral triangle
D)isosceles triangle

Question 10

If 6LJK ÷ 6PNM which of the following conclusion is NOT true?

A)LJ = PN
B)zL = zP
C)zK = zN
D)KL = PM

Question 11

Given 6ABC with sides AB = 10, BC = 14, and AC = 6, which is the largest angle?

A)zC
B)zABC
C)zB
D)zBAC

Question 12

Name the triangle whose sides measure 18 cm, 22 cm, and 18 cm.

A)right
B)scalene
C)equilateral
D)isosceles

Question 13

If the sides of a triangle measure 15 m, 18 m, and 22 m, what kind of triangle is it?

A)equilateral triangle
B)right triangle
C)isosceles triangle
D)scalene triangle

Question 14

If the sides of a triangle measure 12 m, 12 m, and 1,200 cm, what kind of triangle is it?

A)scalene triangle
B)right triangle
C)isosceles triangle
D)equilateral triangle

Question 15

Given 6ABC~6DEF, AB = 12, DE = 4, BC = 24, what does EF equal?

A)8
B)2
C)9
D)72

Question 16

Select the specific name for this figure.

A)equilateral triangle
B)acute triangle
C)scalene triangle
D)right triangle

Question 17

6ABC~6 DEF, zA = zD, zB = zE. Find y

A)2.8
B)4
C)5.6
D)4.72

Question 18

Question 19

Find the height of a flagpole if its shadow measures 12 m when a meter stick casts a shadow of .7 m.

Question 20

What is the name of a triangle with two equal sides?

A)right triangle
B)scalene triangle
C)equilateral triangle
D)isosceles triangle

Question 21

A 35-foot length of a roadway goes over a hill that is 20 feet high. What horizontal length does it cover? Round to the nearest foot.

Question 22

6ABC~ 6DEF, zA ÷ zD, zB ÷ zE. Find x.

A)4.72
B)2.8
C)4
D)5.6

Question 23

If a square nut has a diagonal measure of 4 inches, what is the measure of each side? (Round answer to nearest tenth.)

Question 24

A triangular city block is 360 ft on one side and 375 ft on the second side.
What is the area of the block?

Question 25

Given 6ABC~6DEF, AB = 2.2, DE = 0.6, BC = 2.4, what does EF equal?

A)7.67
B)0.55
C)0.65
D)8.8

Question 26

Find the height of a tree that makes a 40-foot shadow when a 5 ft - 3 in. pole is used to make a shadow of 3 feet.

A)70.7 feet
B)42.8 feet
C)22.9 feet
D)70 feet

Question 27

Find the magnitude of the vector It (total current)in the given figure. Round to the nearest tenth.

A)9.6 milliamps
B)6.8 milliamps
C)46.8 milliamps
D)3.1 milliamps

Question 28

Find the slant height of a cone if the diameter of the base is 24.66 mm and the height is 12.45 mm.

A)37.11 mm
B)8.49 mm
C)17.52 mm
D)21.29 mm

Question 29

A triangular city block is 360 ft on one side and 375 ft on the second side.
What is the length of the block?

Question 30

What must be the length of a rafter that has a rise of 6 feet with a run of 8 feet?

Question 31

Using 6ABC~6AED, find the length of DE.

A)9.6
C) 48
D) 15

Question 32

Alice and Ted want to cut down a tree in their backyard. If the shadow on a 4-foot stick makes a length of 2.5 feet, how tall is the tree to the nearest foot whose shadow is 38 feet?

A)24 ft
B)95 ft
C)61 ft
D)152 ft

Question 33

A triangular city block is 360 ft on one side and 375 ft on the second side.
What is the perimeter of the block?

Question 34

A triangular city block is 360 ft on one side and 375 ft on the second side.
What is the length of the third side?

Question 35

Determine BC if AC = 4.2 ft and AB = 9.1 ft. Round to the nearest tenth.

A)8.1 ft
B)4.7 ft
C)59.3 ft
D)65.2 ft

Question 36

A capsule is made with a rectangular solid base that has dimensions of 14.4 cm × 14.4 cm × 18.6 cm. The cone sits on top and has a slant height of 23.6 cm. Determine the volume of the capsule.

Question 37

Determine AB if AC = 26 cm and BC = 24 cm.

A)10 cm
B)2 cm
C)50 cm
D)35 cm

Question 38

Find A if C = 8 and B = 5. Round the answer to the nearest thousandth.

Question 39

Solve for b.

A)
B)
C)
D)

Question 40

Determine AB if AC = 6 cm and BC = 15 cm.

A)13.75 cm
B)21 cm
C)16.16 cm
D)261 cm

Question 41

Find A if C = 4 and B = 2. Round answer to the nearest thousandth.

Question 42

Find the number of degrees of each angle of a regular decagon (10 sides).

A)225°
B)10°
C)144°
D)180°

Question 43

Determine BC if AC = 4.71 ft and AB = 10.28 ft. Round to the nearest hundredth.

A)11.31 ft
B)5.57 ft
C)9.14 ft
D)2.32 ft

Question 44

Find the number of degrees in each angle of a regular octagon.

A)240°
B)135°
C)120°
D)180°

Question 45

A ladder is leaning against the wall of a house with the bottom of the ladder 5 feet from the wall. The top of the ladder extends 12 feet up the wall. How long is the ladder?

Question 46

Find the hypotenuse of a right triangle whose legs measure 5 and 12 m.

Question 47

A cannery processes green beans. One of the pieces of equipment it uses is called a sniper because it snips off the ends of the green beans. Inside the 6-foot drum is a series of triangular shaped blades, 3 in. on a side, connected in a row the length of the drum. What is the area covered by the blades inside the sniper drum?

Question 48

A conduit ABCD must be made so that zCBE is 45°. If BE = 5 cm and AK = 16 cm, find the length of the conduit to the nearest thousandth of a centimeter.

A)19.660 cm
B)14.536 cm
C)23.071 cm
D)18.071 cm

Question 49

What is the measurement needed of the third side of a triangle with two sides of 10 mm and 10 mm to make it a 45°, 45°, 90° triangle?

A)7.07 mm
B)14.14 mm
C)10 mm
D)17.32 mm

Question 50

The rafters of a house make a 30° angle with the joists. If the rafters have a 20-in. overhang and the center of the roof is 12 ft above the joists, how long must the rafters be cut?

A)21 ft 8 in.
B)26 ft
C)24 ft 8 in.
D)25 ft 8 in.

Question 51

A piece of round steel is milled to a point at one end. The angle formed by the point is the angle of taper. If the steel has a 22-mm diameter and a 60° angle of taper, find the length c of the taper.

A)19.1 mm
B)21 mm
C)22 mm
D)11 mm

Question 52

Given a 30°, 60°, 90° triangle, find the side opposite the 60º if the hypotenuse is 22.4 m.

A)11.2 m
B)6.5 m
C)38.8 m
D)19.4 m

Question 53

A 10-ft length of drainpipe has a cross-section as indicated below. What volume of water would the pipe hold?

Question 54

Find the total length to the nearest inch of the conduit ABCD if XY = 6 ft, CE =14 in., and zCBE = 30°

A)6 ft 2 in.
B)6 ft
C)6 ft 4 in.
D)8 ft 4 in.

Question 55

A V-slot forms a triangle whose angle at the vertex is 60°. The depth of the slot is 24 mm. Find the width of the V-slot.

A)12 mm
B)24 mm
C)13.9 mm
D)27.7 mm

Question 56

Find the length of the wire attached to a light pole 2.5 feet from the top of the light pole. The pole is 36 feet high. The wire is secured with a two-foot screw anchor 18 feet from the
Base of the pole.

A)31.2 ft
B)40.2 ft
C)38.0 ft
D)28.3 ft

Question 57

Determine AB if AC = 123.4 m and BC = 87.6 m. Round to the nearest tenth.

A)418.9 m
B)211.0 m
C)86.9 m
D)151.3 m

Question 58

Given a 45°, 45°, 90° triangle, find the hypotenuse if a leg is 12.3 cm.

A)17.39 cm
B)12.3 cm
C)8.70 cm
D)21.30 cm

Question 59

A manufacturer recommends attaching a guy wire to its 40-ft antenna at a 45° angle. If the antenna is installed on a flat surface, how long must the guy wire be (to the nearest foot)if it is attached to the antenna 4 ft from the top.

A)51 ft
B)57 ft
C)50 ft
D)36 ft

Question 60

What is the measurement needed of the third side of a triangle with two sides of 7 m and 14 m to make it a 30°, 60°, 90° triangle?

A)4.04 m
B)9.90 m
C)12.12 m
D)3.5 m

Question 61

Find x if the distance between the points (x, 5)and (2, -3)is 10.

A)8 or -4
B)11.798 or -7.798
C)4 or 0
D)6 or -6

Question 62

Find the distance between the points (-3, 2)and (-5, 6).

A)6
B)2
C)4.472
D)11.314

Question 63

Given the coordinates of three points that form a triangle, what formula must be used to determine if the triangle is equilateral?

A)midpoint
B)equation of a line
C)slope
D)distance

Question 64

Taylor used a hexagonal stock with a 2-in. distance across the flats to mill a new hexagonal rod as illustrated in the cross-section. Assume the vertices of the inside hexagon are the midpoints of the original hexagon's sides. What is the length of one side of the new hexagon?

A)1.73 in.
B)1 in.
C)2 in.
D)0.87 in.

Question 65

One end of a shaft 40 mm in diameter is milled as shown in the given figure. Find the radius of the smaller circle.

A)10 mm
B)23.67 mm
C)5 mm
D)20 mm

Question 66

Ford milled a square metal rod so that a circle is formed at the end. If the square cross-section is 2.4 mm across the corners, what is the diameter of the circle?

A)2.4 mm
B)0.849 mm
C)1.697 mm
D)3.394 mm

Question 67

Taylor used a regular hexagonal stock with a 2-in. distance across the flats to mill a new hexagonal rod as illustrated in the cross-section. Assume the vertices of the inside hexagon are the midpoints of the original hexagon's sides. What is the area milled off the original hexagon to create the new one?

Question 68

Find the difference in the area of a circle circumscribed about a regular hexagon with sides of 10 cm and the area of the circle inscribed inside the same hexagon.

Question 69

Find the difference in the area of a circle circumscribed about a square with sides of 10 cm and the area of the circle inscribed inside the same square.

Question 70

Find the distance between the points (1, -2)and (-5, -6).

A)7.211
B)10
C)4.472
D)8.944

Question 71

A circle is inscribed inside a square that has an area of 324 mm2. What is the radius of the circle?

Question 72

Find the circumference of a circle inscribed in an equilateral triangle if the height of the triangle is 14 in.

A)21.99 in.
B)87.96 in.
C)29.32 in.
D)43.98 in.

Question 73

The end of a 30 mm-diameter round rod is milled as shown in the given figure. Find the area of the square.

Question 74

A circle is inscribed inside a square that has an area of 256 in2. What is the area of the circle? Round to the nearest inch.

Question 75

Find the distance between the points (5, -1)and (9, 2).

A)14.036
B)7
C)5
D)4.123

Question 76

A sprinkler created a circular path around a hexagonal field of grain. What is the area that is watered that does not have any grain planted in it?

Question 77

Find the distance between the points (-4, 7)and (8, 2).

A)7
B)9.849
C)6.403
D)13

Question 78

The diameter of a circle inscribed in a square in the same as the length of one side of the square. Find the diameter of a circle inscribed in a square if the area of the square is 81 in2 (round to the nearest hundredth).

Question 79

Find the difference in the area of a circle circumscribed about an equilateral triangle with sides of 10 cm and the area of the circle inscribed inside the same equilateral triangle.