Review for Test over Triangle Inequalities, Special Right Triangles, Pyth Thm in 3D, and Trig
1) The figure below is not drawn to scale.
2) In ∆ABC, AB = 3x + 20, BC = 75, and AC = 2x – 10.
What is the longest segment in the diagram?
Find the possibilities for x.
E
45˚
B
40˚
75˚ 50˚
D
C
3) Is it possible for a triangle to have sides of the given lengths? If yes, classify each triangle with the given side
lengths as acute, right or obtuse.
a)_________ 1, 2, √2
b) ______________12, 14, 12
c)_____________ 6, 10, 18
4) Two sides of a triangle are 5 inches and 16 inches.
Describe the lengths possible for the third side.
5) In triangle DEF, the perimeter is 38. If DE = 2x + 3,
EF = 3x, and DF = x – 1, list the angles in order from
smallest to greatest.
6) In ABC, mA = x2 + 6, mB = 8x + 12, and
mC = 5x + 22. Find x and the measure of each angle.
Which is the shortest side?
7) m1 = 38o and m2 = 3x + 5. Write the inequality
that describes the range
96
9
of possible values for x.
12
12
1
2
60
8) State whether AB or BD is the greater measure.
(a)
A
60
D
(b)
17
70
C
20
17
20
D
96
A
C
105
46
B
B
9) In WZY, segment ZX is a median. If mWXZ = x2 + 4x + 14 and mZXY = 9x – 2.
Which side is longer, WZ or ZY?
W
Z
X
Y
10) Find the length of the altitude of an equilateral
triangle with perimeter 48.
11) Find the perimeter of a square whose diagonal is
6.
12) MR = 18. Find the length of MP
13) Find AM = __________
Find the altitude of trapezoid TAMU = __________
R
T
135
Q
A
12
30
M
P
U
45o
60o
M
18
14) Terry drove 5 miles east, 7 miles north, 6 miles
east, 2 miles south, and 1 mile east. How far is he
from his starting point?
15) An isosceles trapezoid has a longer base with
length 35. The legs have lengths 15 and the altitude
of the trapezoid has length 12. Find the length of the
shorter base.
16) A regular square pyramid has a base with a
perimeter of 40. The lateral edge has a length of 20.
Find the altitude and the slant height.
17) The dimensions of a rectangular solid are in the
ratio 3:4:5. If the interior diagonal is 200 2 , find the
three dimensions.
E
Altitude = _________
Slant height = ________
D
F
A
C
B
18) A radio tower 200 ft. high casts a shadow 75 ft.
long. What is the angle of elevation of the sun?
19) A ladder 14 feet long rests against the side of a
building. The base of the ladder rests on level ground
2 feet from the side of the building. What angle does
the ladder form with the ground?
20) A lighthouse is 100 feet tall. The angle of
depression from the top of the lighthouse to one boat
is 24°. The angle of depression to another boat is 31°.
How far apart are the boats?
21) A 24-foot ladder leaning against a building forms
an 18˚ angle with the side of the building. How far is
the base of the ladder from the base of the building?
Answers:
1. BE
2. 13 < x < 45
3. obtuse, acute, not a triangle
4. between 11 and 21
5. x = 6 so DE = 15, EF = 18, DF = 5. Angles in order of smallest to largest:
E, F, D
6. x = 7, mA = 55, mB = 68, mC = 57 so BC is shortest side.
7. –5/3 < x < 11
8. AB, BD
9. x = 8 so WZ is longer than ZY.
10. 8 3
11. 12 2
12. MP = 9 3 - 9
13. AM = 6 6 ; altitude = 6 3
14. 13 miles
15. 17
16. Alt. = 5 14 ; slant height = 5 15
17. 120 x 160 x 200
18. 69.4o
19. 81.8o
20. 165 feet
21. 7.4 ft