Answer Key
Geometry Chapter 7 Final Review Answer Key
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University:
University of North Georgia -
Course:
MATH 3110 | Informal Geometry for Teachers Academic year:
2021
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Views:
146
Pages:
21
Author:
larbiwxcvbn
Geometry CP
Chapter 7 Final Review
Name:
Find the unknown side length. Write your answer in simplest radical form.
1. x = 13
2. x = 72
3. x = 39
4. x = 12
Find the indicated value. Write your answer in simplest radical form.
5. Randy made a ramp for his dog to get into the bed of his truck. The ramp is 6 ft long and the bed of the truck is 3 ft above the ground. Approximately how far from the back of the truck does the ramp touch the ground?
A. 3 ft
B. 4 ft
C. 5.2 ft
D. 6.7 ft
6. Find the area of the isosceles triangle with side lengths 20 in., 20 in., and 24 in.
Area = 96 in²
7. Find the altitude. Then find the area of the isosceles triangle.
[Image of an isosceles triangle with base 28 and height h]
h = 24
Area = 336 sq units
Find the similarity ratio of the side lengths.
8. 7, 11, and 3/17
9. 2, 2, and 5/2
10. 4.1, 9.2, and 5.6
11. [Image of two similar triangles]
Similarity ratio: 20/11
12. [Image of two similar triangles]
Similarity ratio: 10/8 = 5/4
13. [Image of two similar triangles]
Similarity ratio: 2√10 / 4√10 = 1/2
14. Identify the similar triangles in the diagram.
[Image of a diagram with triangles]
ΔDEF ~ ΔGHI
15. Identify the similar triangles in the diagram.
[Image of a diagram with triangles]
ΔABC ~ ΔDBE
16. Find the value of a.
[Image of a diagram with triangles]
a = 6
17. Skip!
18. Find the values of y, KL, and KM.
[Image of a diagram with triangles]
y = 15
KL = 15
KM = 15√2
19. Find the values of y, XZ, YZ, and XY.
[Image of a diagram with triangles]
y = 26
XZ = 26
YZ = 26√2
XY = 52
Using special right triangles, find the values of the variable(s). Write your answer(s) in simplest radical form.
20. Find the value of the hypotenuse.
[Image of a right triangle with legs 12 and 12]
Hypotenuse = 12√2
21. Find the value of the hypotenuse.
[Image of a right triangle with legs 10√2 and 10√2]
Hypotenuse = 20
22. ΔMNP is a right triangle. Find the length of MP.
[Image of a right triangle with legs 18 and 18]
A. 18 in.
B. 9√2 in.
C. 36 in.
D. 18√2 in.
23. [Image of a right triangle with legs 15 and x]
x = 15
24. [Image of a right triangle with legs 8 and x]
x = 8√3
25. A kite is attached to a 100-foot string as shown in the diagram. How far above the ground is the kite when the string forms the given angle? 1
1.
mi01000971.schoolwires.net
mi01000971.schoolwires.net
[Image of a right triangle with hypotenuse 100 and angle 45 or 30 degrees]
A. m∠1 = 45°
B. m∠1 = 30°
Using special right triangles, find the three trig functions of 45°.
26. [Image of a right triangle with legs 1 and 1]
sin(45°) = √2/2
cos(45°) = √2/2
tan(45°) = 1
27. Using a special right triangle, find the three trig functions of 30°.
[Image of a right triangle with sides 1, √3, and 2]
sin(30°) = 1/2
cos(30°) = √3/2
tan(30°) = √3/3
28. Find all three trig functions of angle B.
[Image of a right triangle with sides 3, 4, and 5]
sin(B) = 3/5
cos(B) = 4/5
tan(B) = 3/4
29. Find all three trig functions of angle P.
[Image of a right triangle with sides 15, 36, and 39]
sin(P) = 15/39 = 5/13
cos(P) = 36/39 = 12/13
tan(P) = 15/36 = 5/12
30. Find all three trig functions of angle F.
[Image of a right triangle with sides 40, 75, and 85]
sin(F) = 40/85 = 8/17
cos(F) = 75/85 = 15/17
tan(F) = 40/75 = 8/15
31. If y = 12 and x = 6, find sin X to the nearest tenth.
[Image of a right triangle with sides x, y, and 12]
sin(X) = 6/12 = 0.5
Find the value of the variable to the nearest tenth.
32. Find the height (x) of the flagpole to the nearest foot.
[Image of a right triangle with height x and base 24]
tan(49°) = x/24
x ≈ 27 feet
33. A lamppost is 11 feet tall. If the angle of elevation through the top of the lamppost to the sun is 49°, about how far is the top of the lamppost from the tip of its shadow?
[Image of a right triangle with height 11 and angle 49°]
tan(49°) = 11/x
x ≈ 9.3 feet
34. A rope, staked 20 feet from the base of a building, goes to the roof and forms an angle of 58° with the ground. How long is the rope?
[Image of a right triangle with base 20 and angle 58°]
sin(58°) = 20/x
x ≈ 23.6 feet
35. A road rises 10 feet in a horizontal distance of 200 feet. What is the angle of elevation?
tan(θ) = 10/200
θ ≈ 2.86°
36. If a = 17 and m∠A = 31°, find b.
[Image of a right triangle with side a = 17 and angle A = 31°]
sin(31°) = b/17
b ≈ 8.7
37. Find x.
[Image of a right triangle with hypotenuse 50 and angle 45°]
x = 50/√2 = 25√2
Geometry Chapter 7 Final Review Answer Key
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