AnswersFall 24 GMS Geometry Concepts and Connections BSolving for Angle Measures of Right Triangles

Solving for Angle Measures of Right Triangles — Cumulative exam Answers

42 verified answers
21
Free Preview

Triangle X Y Z is shown. Angle X Z Y is a right angle. Angle Z X Y is 60 degrees and angle X Y Z is 30 degrees. The length of hypotenuse X Y is 42 and the length of X Z is 21.

Question illustration
A
One-half
Option A
B
StartFraction StartRoot 3 EndRoot Over 2 EndFraction
Option B
C
StartRoot 3 EndRoot
Option C
D
StartFraction 2 Over 1 EndFraction
Option D
22
Free Preview

There are 14 dogs in a particular class at a dog show. Blue, red, yellow, and white ribbons will be awarded to the first through fourth place finishers, respectively. In how many different ways can the ribbons be awarded?

A
1,001
B
6,006
C
24,024
D
38,416
23

On a coordinate plane, triangles R S T and L M N are shown. Triangle R S T has points (5, 5), (2, 1), and (1, 3). Triangle L M N has points (0, negative 1), (2, negative 4), and (negative 2, negative 3).

Question illustration
A
The area of △RST is 2 square units less than the area of △LMN.
B
The area of △RST is equal to the area of △LMN.
C
The area of △RST is 2 square units greater than the area of △LMN.
D
The area of △RST is 4 square units greater than the area of △LMN.
24

Including Jose, there are eight people in his family.If order matters, how many ways can he arrange his family members into a row of five seats if Jose must sit in the first seat?

A
35
B
840
C
1,680
D
2,620
25

A guidance counselor reports that in a given semester, the probability that a student chooses art as an elective is 15 percent, the probability that a student chooses art or drama is 20 percent, and the probability that a student chooses both art and drama is 2 percent.What is the probability that a student chooses drama as an elective?

A
5 percent
B
7 percent
C
33 percent
D
37 percent
26

The volume of a cone is 3πx3 cubic units and its height is x units.Which expression represents the radius of the cone’s base, in units?

A
3x
B
6x
C
3πx2
D
9πx2
27

Jude has a deck of playing cards. He is asked to remove one card at random, then a second card. What could Jude do between the events to ensure they are dependent?

A
He could get a new, complete deck of playing cards.
B
He could return the first card back to the original deck.
C
He could put the first card he removed into his pocket.
D
He could choose to not remove the second card.
28

People at the state fair were surveyed about which type of lemonade they preferred. The results are shown below.Pink lemonade: 156 males, 72 femalesYellow lemonade: 104 males, 48 females

A
P(pink lemonade | female) = P(pink lemonade) = 0.6.
B
P(female | pink lemonade ) = P(pink lemonade) = 0.3.
C
P(pink lemonade | female) = 0.3 and P(pink lemonade) = 0.6.
D
P(female | pink lemonade ) = 0.3 and P(pink lemonade) = 0.6.
29

On a coordinate plane, triangles A B C and D E F are shown. Triangle A B C has points (4, 2), (7, 2), (4, 6). Triangle D E F has points (negative 2, negative 1), (4, negative 3), and (4, negative 1).

Question illustration
A
The area of △ABC is 1 square unit less than the area of △DEF.
B
The area of △ABC is equal to the area of △DEF.
C
The area of △ABC is 1 square unit greater than the area of △DEF.
D
The area of △ABC is 2 square units greater than the area of △DEF.
30

Which is the graph of y – 3 = (x + 6)?

Question illustration
A
Option
B
Option
C
Option
D
Option
31

Kite E F G H is inscribed within a rectangle. Points F and H are midpoints of the sides of the rectangle. Points E and G are parallel to the side of the rectangle.

Question illustration
A
The area of EFGH is of the area of the rectangle if E and G are not midpoints.
Option A
B
The area of EFGH is of the area of the rectangle only if E and G are midpoints.
Option B
C
The area of EFGH is always of the area of the rectangle.
Option C
D
The area of EFGH is always of the area of the rectangle.
Option D
32

Rectangle ABCD was dilated to create rectangle A'B'C'D.

Question illustration
A
6 units
B
7.6 units
C
9.5 units
D
12 units
33

A regular pentagon has side lengths of 14.1 centimeters and an apothem with length 12 centimeters.

Question illustration
A
288 cm2
B
342 cm2
C
432 cm2
D
691 cm2
34

Triangle A B C is shown. Angle B C A is a right angle. The length of C B is 5 inches and the length of C A is 7 inches.

Question illustration
A
1.4° and 88.6°
B
18.6° and 71.4°
C
35.5° and 54.5°
D
44.4° and 45.6°
35

Triangle ABC is a right triangle and sin(53o) = . Solve for x and round to the nearest whole number.

Question illustration
A
cos(53o) =
Option A
B
cos(53o) =
Option B
C
cos(53o) =
Option C
D
cos(53o) =
Option D
36

A cone has a circular base with a diameter of 18 inches. The height of the cone is 40 inches.What is the approximate lateral area of the cone? Use 3.14 for π and round to the nearest whole number.

A
565 square inches
B
580 square inches
C
1,131 square inches
D
1,159 square inches
37

The side lengths of triangle RST are 5, 12, and 13. Which set of ordered pairs form a triangle that is congruent to triangle RST?

A
(–3,–2),(–3,11),(9,–2)
B
(1,–3),(6,–3),(6,10)
C
(2,–1)(7,–1),(2,11)
D
(5,1),(1,13),(12,1)
38

An urban planner collects data on how park trails are used by residents. The planner looks at two trails: one that winds through an urban area and another in a suburban park. The table shows the number of users who walk, jog, or bike the trail. Activity WalkJogBikeTotalType of ParkUrban765823157Suburban1257642243 Total20113465400What proportion of suburban park users bike on the park trail?

A
0.1050
B
0.1728
C
0.6075
D
0.6461
39

Pentagon ABCDE is dilated according to the ruleDO,3(x,y) to create the image pentagon A'B'C'D'E', which is shown on the graph.

Question illustration
A
(-1, 1)
B
(-1, 2)
C
(-9, 6)
D
(-9, 18)
40

Jaxon has a bag of marbles. He draws one marble from the bag. Before drawing another marble from the bag, what could Jaxon do to ensure that the events are independent of each other?

A
keep the marble he initially drew from the bag
B
return the marble he initially drew from the bag
C
add more marbles to the bag
D
remove all marbles that are the same color as the first one

Did you find these answers helpful?

More from this Course

Quiz
10 verified answers

Solving for Angle Measures of Right Triangles (Sec 8-5)

RC
25 verified answers

Cumulative Exam

Quiz
10 verified answers

Pre-Test