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REVIEW SHEET # 10
NAME__________________________________________DATE___________________PER._____
REVIEW SHEET #10: RIGHT TRIANGLES
PART 1. PYTHAGOREAN THEOREM
For each of the following, find the value of ‘x’.
__________1.
x
5
12
__________2.
x
6
10
__________3.
x
x
6 2
x
x
24
__________4.
7
x
__________5.
A rectangle has a diagonal of 2 cm and a length of 3 cm. Find its width.
__________6.
Find the length of a diagonal of a square with a perimeter of 16.
PART 2. CONVERSE OF THE PYTHAGOREAN THEOREM
Tell whether a triangle with sides of given lengths can be formed, and is so, classify is
as acute, right, or obtuse.
7. Can a triangle be formed?
YES
or
Classification:
NO
Side lengths: 9, 9, and 3
REVIEW SHEET # 10 Pg. 2
8. Can a triangle be formed?
YES
or
Side lengths: 8, 8 3 , 16
NO
Classification:
9. Can a triangle be formed?
YES
or
Side lengths: 11, 11, 15
NO
Classification:
10. Can a triangle be formed?
YES
or
Side lengths: 8, 14, 22
NO
Classification:
PART 3. 45-45-90 & 30-60-90 TRIANGLES
For each of the following, find the indicated lengths.
F
11. FI = __________
BI = __________
6
45
I
B
C
12. CI = __________
10 2
IA = __________
45
I
A
D
13. DE = __________
EA = __________
13
60 A
E
F
14. FE = __________
60
ED = __________
3
E
30
D
REVIEW SHEET #10 Pg. 3
W
15. SW = __________
9 3
SA = __________
S
ST = __________
60
45
A
TA = __________
T
PART 4. TRIGONOMETRIC RATIOS
Use the diagram to express each ratio as a fraction in simplest form.
16. __________
Find sinL.
L
17. __________
Find cosL.
9
18. __________
15
Find tanL.
M
19. __________
Find sinN.
20. __________
Find cosN.
21. __________
Find tanN.
12
N
Using your trigonometric table, find the value of ‘x’ in each of the following.
22. x = __________
63
12
x
23. x = __________
100
61
x
PART 5. REVIEW PROBLEMS
24. AB = __________
B is between A and C. If AB = 2x – 5, BC = x – 2, and AC = 20,
find AB.
REVIEW SHEET # 10 Pg. 4
25. x = __________
BD bisects ABC. mABC = 67 and mABD = (3x – 1). Find
the value of ‘x’.
26. x = __________
1 and 2 are same side interior angles formed by 2 parallel
lines and a transversal. If m1 = (4x – 3) and m2 = (3x + 1),
find the value of ‘x’.
27. measure = ________
Find the measure of each exterior angle of a regular dodecagon.
28. x = __________
In rhombus ABCD, AB = 4x – 2 and BC = x + 7. Find the value
of ‘x’.
PART 6.
Find the best answer for each of the following. Clearly circle/bubble in your answer as
necessary. Work must by shown in order to receive credit.
Hilltop Parkway
29. In a town there is a small park shaped
like a triangle. The side of the garden that
faces River Road is 80 feet in length. The
side that faces Hilltop Parkway is 30 feet in
length.
Willow Drive
River Road
What is the approximate length of the
side that faces Willow Drive?
30. A square park has a diagonal walkway
from one corner to the other. If the
walkway is about 38 yards long, what is
the approximate length of each side of the
park?