Geometry Chapter 7 Review
Right Triangles
Name:
Use this review to help prepare for the Chapter 7 Test. The answers are attached at the
end of the document.
1. The tangent of ∡𝐵 is _____.
2. ∆𝐴𝐵𝐶 is a right triangle. AB = _____.
3. Find the altitude of an isosceles triangle with base 10 and congruent sides of length 9.
4. Find sin P, cos P, tan P.
25
7
P
24
5. For each set of numbers, determine whether the numbers represent the lengths of the
sides of an acute triangle, a right triangle, an obtuse triangle, or no triangle.
A. 6, 9, 12
B. 3.2, 4.2, 5.2
C. 38, 25, 13
D. 3, 4, 7
6. Which of the following cannot be the lengths of a 30-60-90 triangle?
[A]
9
9
, 9,
3
2
2
[C] 8, 16, 8 3
[B]
4 8 4
, ,
3
3 3 3
[D] 5,
5
,5 3
2
Geometry Chapter 7 Review
Right Triangles
Name:
7. For the triangle shown below, the Pythagorean Theorem states that _____.
[A] e2  f 2  g 2
[C] f 2 – g 2  e2
[B] e = f + g
[D] e2  f 2  g 2
8. Classify a triangle with sides 10, 10, and 18 as acute, obtuse, or right.
9. The shorter leg of a 30-60-90 triangle is 9.7 inches long. Find the perimeter.
10. Which triangle below is NOT congruent to the others?
[A]
[B]
[C]
[D]
3
3
5
30
4
5
3
4
3
11. In a 45°-45°-90° triangle, the ratio of the length of the hypotenuse to the length of a
side is _____.
[A] 2:1
[B] 1:1
[C]
2 :1
[D]
3 :1
12. In a 30°-60°-90° triangle, the ratio of the length of the hypotenuse to the length of the
shorter side is _____.
[A]
3 :1
[B]
2 :1
[C] 2:1
[D] 2: 3
13. To find the height of a tower, a surveyor positions a transit that is 2 m tall at a spot 30
m from the base of the tower. She measures the angle of elevation to the top of the
tower to be 59  . What is the height of the tower, to the nearest meter?
Geometry Chapter 7 Review
Right Triangles
Name:
14. If EFGH is a rectangle, what is FH?
15. The city commission wants to construct a new street that connects Main Street and
North Boulevard as shown in the diagram below. The construction cost has been
estimated at $110 per linear foot. Find the estimated cost for constructing the street.
(1 mile = 5280 ft)
North Blvd.
(new street)
9 mi
W
M ain St. E
5 mi
S
16. Find the area of this right triangle if b  8 and c  10.
c
a
b
17. Find the value of x, to the nearest whole number. (not drawn to scale)
G
15
53°
I
x
H
18. Solve the right triangle:   30 and a  18; find  , b, and c
c

a

b
Geometry Chapter 7 Review
Right Triangles
Name:
19. Find the value of x and y.
x
6
60°
y
20. Name 3 Pythagorean Triples (no multiples).
21. A radio station is going to construct a 6-foot tower for a new antenna. The tower will
be supported by three cables, each attached to the top of the tower and to points on the
roof of the building that are 8 feet from the base of the tower. Find the total length of the
three cables. Draw it.
[A] 50 ft
[B] 40 ft
[C] 30 ft
[D] 10 ft
22. Choose the sets that are possible side lengths of a right triangle.
A. 1, 1, 2
B. 1, 1, 2 C. 3, 4, 7
D. 3, 4, 5
23. The length of the diagonal of a square is 22. What is the length of each side?
24. Find the value of x and y .
y
3
30°
x
25. What is the length of an altitude of an equilateral triangle with side lengths 8 3?
26. If the side lengths of a triangle are 7, 6, and 9, the triangle _____.
[A] is an acute triangle
[B] is a right triangle
[C] cannot be formed
[D] is an obtuse triangle
27. Write cos A.
B
13
A
12
[A]
12
5
[B]
5
12
[C]
12
13
[D]
5
13
5
C
Geometry Chapter 7 Review
Right Triangles
Name:
28. Find tan S.
29. Liola drives 21 km up a hill that is at a grade of 13. What horizontal distance, to the
nearest tenth of kilometer, has she covered?
[A] 4.7 km
[B] 12.1 km [C] 4.8 km
[D] 20.5 km
30. A baseball “diamond” is a square of side length 90 feet. How far is the throw, to one
decimal place, from home plate to second base?
31. Which set of lengths cannot form a right triangle?
[A] 7 mm, 8 mm, 10 mm
[B] 3 mm, 4 mm, 5 mm
[C] 6 mm, 8 mm, 10 mm
[D] 12 mm, 16 mm, 20 mm
32. A telephone pole breaks and falls as shown.
To the nearest foot, what was the original height of the pole?
7 ft
10 ft
[A] 19 ft
[B] 20 ft
[C] 21 ft
[D] 18 ft
Geometry Chapter 7 Review
Right Triangles
Name:
33. What is the length of the diagonal of a square with side lengths 7 2?
34. Find the perimeter and area of Trapezoid ABCD.
A
32 𝑚
B
25 𝑚
D
36°
30°
C
35. List the angle and sides of ∆𝐴𝐵𝐶 from least to greatest
C
A
65
56
B
36. List the angle and sides of ∆𝐴𝐵𝐶 from least to greatest
C
6
A
7
8
B
37. What are the possible lengths of a the third side, x if two sides of a triangles have sides lengths
of:
A: 3 and 13
B: 24 and 32
38. Which side lengths allow you to construct a triangle?
[A] 2, 3, and 8
[B] 6, 8, and 10
[C] 4, 1, and 9
[D] 7, 2, and 2
Geometry Chapter 7 Review
Right Triangles
Name:
39. Two sides of a triangle have lengths 8 and 11. What are the possible lengths of the third side
x?
40. Two sides of a triangle have lengths 7 and 13. The third side has a length that is ______.
41. Which of these lengths could be the sides of a triangle?
[A] 13 cm, 19 cm, 4 cm
[B] 19 cm, 9 cm, 11 cm
[C] 19 cm, 13 cm, 5 cm
[D] 9 cm, 19 cm, 10 cm
Geometry Chapter 7 Review
Right Triangles
[1]
95
7
[2] 117
[3] 56 or 2 14
7
24
[4] sin 𝑃 = 25 , cos 𝑃 = 25 ,
7
tan 𝑃 =
24
[5] A. obtuse
B. acute
C. right
D. no
[6] [D]
[7] [D]
[8] obtuse
[9] (291
.  9.7 3) in.
=45.9 in.
Name:
[10] [B]
[11] [C]
[12] [C]
[13] 52 m
[14] 65
[15] $5,979,701.99
[16] 24
[17] 12
[18] 𝛽 = 60°
𝑏 = 18 3 = 31.18
𝑐 = 36
[19] x = 6 3 , y = 12
[20]
[21] 30 feet
[22] B and D
[23] 11 2
[24] x = 3 3, y = 6
[25] 12
[26] [A]
[27] [C]
4
[28]
7
[29] [D]
[30] 127.3 ft
[31] [A]
[32] [A]
[33] 14
[34] Perimeter = 149.12 m
Area = 642.85 m2
[35] ∡𝐵, ∡𝐶, ∡𝐴; 𝐴𝐶 , 𝐴𝐵 , 𝐵𝐶
[36] ∡𝐵, ∡𝐴, ∡𝐶; 𝐴𝐶 , 𝐵𝐶 , 𝐴𝐵
[37] A. 10 < 𝑥 < 16
B. 8 < 𝑥 < 56
[38] B
[39] 3 < 𝑥 < 19
[40] 6 < 𝑥 < 20
[41] B