AnswersOH-Geometry BArea and Perimeter of Triangles

Area and Perimeter of Triangles — Unit test Answers

25 verified answers
1
Free Preview

Law of sines:

Question illustration
A
only 90°
B
only 155°
C
20° and 110°
D
45° and 135°
2
Free Preview

The blades of a windmill turn on an axis that is 35 feet above the ground. The blades are 10 feet long and complete two rotations every minute. Which of the following equations can be used to model h, the height in feet of the end of one blade, as a function of time, t, in seconds? Assume that the blade is pointing to the right, parallel to the ground at t = 0 seconds, and that the windmill turns counterclockwise at a constant rate.

A
h = negative 10 sine (StartFraction pi Over 15 EndFraction t) + 35
Option A
B
h = negative 10 sine (Pi t) + 35
Option B
C
h = 10 sine (StartFraction pi Over 15 EndFraction t) + 35
Option C
D
h = 10 sine (Pi t) + 35
Option D
3

Heron’s formula: Area =

Question illustration
A
27 square units
B
38 square units
C
364 square units
D
728 square units
4

Law of cosines: a2 = b2 + c2 – 2bccos(A)

Question illustration
A
35°
B
45°
C
55°
D
65°
5

The law of cosines for RST can be set up as 52 = 72 + 32 – 2(7)(3)cos(S). What could be true about RST?Law of cosines: a2 = b2 + c2 – 2bccos(A)

Question illustration
A
r = 5 and t = 7
B
r = 3 and t = 3
C
s = 7 and t = 5
D
s = 5 and t = 3
6

Triangle ABC is a sketch of a triangular flower bed that has an area of 65.1 square feet.Trigonometric area formula: Area =

Question illustration
A
17 feet
B
33 feet
C
40 feet
D
50 feet
7

The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet. Which of the following equations can be used to model the height as a function of time, t, in hours? Assume that the time at t = 0 is 12:00 a.m.

A
h = 0.5 cosine (StartFraction pi Over 12 EndFraction t) + 9.5
Option A
B
h = 0.5 cosine (StartFraction pi Over 6 EndFraction t) + 9.5
Option B
C
h = cosine (StartFraction pi Over 12 EndFraction t) + 9
Option C
D
h = cosine (StartFraction pi Over 6 EndFraction t) + 9
Option D
8

Law of sines:

Question illustration
A
15°
B
30°
C
45°
D
60°
9

Two teams are pulling a heavy chest, located at point X. The teams are 4.6 meters away from each other. Team A is 2.4 meters away from the chest, and Team B is 3.2 meters away. Their ropes are attached at an angle of 110°.Law of sines:

Question illustration
A
StartFraction sine (uppercase A) Over 2.4 EndFraction = StartFraction sine (110 degrees) Over 4.6 EndFraction
Option A
B
StartFraction sine (uppercase A) Over 4.6 EndFraction = StartFraction sine (110 degrees) Over 2.4 EndFraction
Option B
C
StartFraction sine (uppercase A) Over 3.2 EndFraction = StartFraction sine (110 degrees) Over 4.6 EndFraction
Option C
D
StartFraction sine (uppercase A) Over 4.6 EndFraction = StartFraction sine (110 degrees) Over 3.2 EndFraction
Option D
10

Law of cosines: a2 = b2 + c2 – 2bccos(A)

Question illustration
A
34°
B
41°
C
51°
D
56°
11

Trigonometric area formula: Area =

Question illustration
A
70.5 square units
B
111.3 square units
C
185.4 square units
D
222.5 square units
12

A kite is made up of two isosceles triangles, KIT and KET, with the lengths shown. The top triangle of the kite, ΔKIT, is made from approximately 17 square inches of material.Heron’s formula: Area =

Question illustration
A
31 square inches
B
34 square inches
C
48 square inches
D
62 square inches
13

Law of cosines: a2 = b2 + c2 – 2bccos(A)

Question illustration
A
92 = y2 + 192 – 2(y)(19)cos(41°)
B
y2 = 92 + 192 – 2(y)(19)cos(41°)
C
92 = y2 + 192 – 2(9)(19)cos(41°)
D
y2 = 92 + 192 – 2(9)(19)cos(41°)
14

The blades of a windmill turn on an axis that is 30 feet from the ground. The blades are 10 feet long and complete 2 rotations every minute. Write a sine model, y = asin(bt) + k, for the height (in feet) of the end of one blade as a function of time t (in seconds). Assume the blade is pointing to the right when and that the windmill turns counterclockwise at a constant rate.

Question illustration
A
y = 30 sine (StartFraction pi Over 15 EndFraction t) + 10
Option A
B
y = 30 sine (StartFraction pi Over 15 EndFraction t) + 30
Option B
C
y = 10 sine (StartFraction pi Over 15 EndFraction t) + 10
Option C
D
y = 10 sine (StartFraction pi Over 15 EndFraction t) + 30
Option D
15

Which measures are accurate regarding triangle JKL? Select two options.

A
m∠K = 94°
B
k ≈ 3.7 units
C
k ≈ 4.6 units
D
KL ≈ 2.5 units
E
KL ≈ 3.2 units
16

The height, h, in feet of a ball suspended from a spring as a function of time, t, in seconds can be modeled by the equation . Which of the following is the graph of this equation?

Question illustration
A
On a coordinate plane, a curve crosses the y-axis at (0, 5). It increases to (2, 8), and then decreases to (6, 2).
Option A
B
On a coordinate plane, a curve crosses the y-axis at (0, 8). It decreases to (4, 2), and then increases to (8, 8).
Option B
C
On a coordinate plane, a curve crosses the y-axis at (0, 5). It increases to (1, 8), and then decreases to (3, 2).
Option C
D
On a coordinate plane, a curve crosses the y-axis at (0, 5). It decreases to (2, 1), and then increases to (3, 8).
Option D
17

Which triangle’s area can be calculated using the trigonometric area formula?

A
Triangle A B C is shown. The length of A C is 28, the length of C B is 24, and the length of A B is 16.
Option A
B
Triangle D E F is shown. The length of E F is 20. Angle F D E is 34 degrees and angle D E F is 108 degrees.
Option B
C
Triangle G H J is shown. The length of G H is 17 and the length of G J is 22. Angle H J G is 47 degrees.
Option C
D
Triangle K L M is shown. The length of K L is 29 and the length of K M is 15. Angle L K M is 35 degrees.
Option D
18

Consider the diagram and the derivation below.Given: In △ABC, AD ⊥ BCDerive a formula for the area of △ABC using angle C.

Question illustration
A
bsin(C)
Option A
B
absin(C)
Option B
C
cbsin(C)
Option C
D
hbsin(C)
Option D
19

Triangle LMN has sides measuring 7 meters and 6 meters and a perimeter of 16 meters.Heron’s formula: Area =

Question illustration
A
3 square meters
B
9 square meters
C
28 square meters
D
34 square meters
20

Law of cosines: a2 = b2 + c2 – 2bccos(A)

Question illustration
A
70°
B
77°
C
80°
D
85°

Did you find these answers helpful?

More from this Course

Quiz
25 verified answers

Unit Test

Quiz
25 verified answers

Unit Test

Quiz
18 verified answers

Unit Test

Area and Perimeter of Triangles — Unit test…