Last Chance Review for Geometry SOL
Recall from chapter 7…
SohCahToa
B
hypotenuse
c
A
b
side adjacent ∠A
1. The 12-foot bed of a dump truck loaded with heavy stone
must rise to an angle of 36° before the stone will spill out.
Approximately how high must the front of the bed rise (x) to
unload?
sin 36° ≈ 0.588
cos 36° ≈ 0.810
tan 36° ≈ 0.727
A 6 ft
B 7 ft
C 9 ft
D 10 ft
2. To determine the distance across a pond, Harry made the
measurements shown in the diagram.
Which is closest to the distance from R to S?
A 3.48 m
B 19.7 m
C 20.3 m
D 113.4 m
3. A cable 48 feet long stretches from the top of a pole to the
ground. If the cable forms a 40° angle with the ground, which
is closest to the height of the pole?
sin 40° ≈ 0.642
A
B
C
D
26.4 ft
30.9 ft
36.8 ft
40.3 ft
cos 40° ≈ 0.766
tan 40° ≈ 0.839
a
C
side
opposite ∠A
Special Right Triangles
Theorem - 45°-45°-90° Triangle Theorem
45°
hypotenuse = leg • 2
x 2
x
45°
x
4. A baseball diamond is in the shape of a square, 90 feet on a side.
What is the direct distance from home plate to second base?
A 90 ft
B 90 2 ft
C 90 3 ft
D 180 ft
Theorem - 30°-60°-90° Triangle Theorem
hypotenuse = 2 • shorter leg
longer leg = shorter leg • 3
5. A billboard is supported by 20-foot lengths of tubing at an
angle of 60°. How far from the base of the billboard is the
bottom end of the brace?
A 5 ft
B 8.7 ft
C 10 ft
D 17.3 ft
6. In the figure, what is the value of x?
A 6
B 6 2
C 6 3
D 12
60°
2x
x
30°
x 3
7. In circle O, ∠RST formed by chord RS and diameter
ST has a measure of 30°. If the diameter is 12 centimeters,
what is the length of chord SR ?
A 12 3 cm
B 12 2 cm
C 6 3 cm
D 6 2 cm
Pythagorean Theorem
c2 = a2 + b2
where c is the hypotenuse!!
8. An airplane is 34 ground miles from the end of the runway (GA)
and 6 miles high (PG) when it begins its approach to the airport. To
the nearest mile, what is the distance (PA) from the airplane to the
end of the runway?
A
B
C
D
41 mi
39 mi
37 mi
35 mi
9. The top of a ladder is leaning on a building at a point 12 feet above the ground; the bottom of the ladder
is 5 feet from the base of the building. What is the length of the ladder?
A
B
C
D
19 ft
17 ft
13 ft
7 ft
Recall from chapter 10 …
Circles
Theorem –
A line is tangent to a circle iff the line is perpendicular
to a radius of the circle at its endpoint on the circle.
P
m
Q
R
Theorem –
Tangent segments from a common external point are congruent.
S
P
T
SR ≅ ST

10. AB is tangent to circle C at B, AB = 15 centimeters, and
the radius of the circle is 8 centimeters.
To the nearest tenth of a centimeter, what is the length of AC ?
A
B
C
D
7.0 cm
12.7 cm
17.0 cm
23.0 cm
11. A, B, and C are points of tangency. AP = 4 and BQ = 8.
What is the measure of PQ ?
A 4
B 8
C 12
D 32
C
Theorem –
EA  EB = EC  ED
Theorem –
EA  EB = EC  ED
B
E
A
B
A
E
C
D
D
Theorem –
EA 2 = EC  ED
B
A
Theorem –
C
If a tangent and a chord intersect
E
C
D
at a point on a circle, then the measure
of each angle formed is half the
measure of its intercepted arc.
2
1
A
12. Chords AB and CD intersect at R. Using the values shown
in the diagram, what is the measure of RB ?
A
B
C
D
6
7.5
8
9.5
13. Secants PB and PD intersect the circle at A and C, respectively.
What is the length of PC ?
A 3
B 4
C 5
D 6

 is 108°.
14. BD is tangent to the circle at B and the measure of AC
What is the measure of ∠CBD ?
A 118°
B 72°
C 36°
D 18°
Recall from chapter 11 …
Area of a sector
A

area of sector AB mAB
=
A
360°
P
r
B
15. A circle for a game spinner is divided into 3 regions as shown.
RP is a diameter. What is the area of the shaded sector ROS if RP = 8?
A
B
C
D
1.5 π
6π
24 π
72 π
A
B
16. Match each construction arcs with the description.
_____ Angle bisector
_____ Perpendicular to a line through a point on the line
_____ Perpendicular bisector
D
C
_____ Perpendicular to a line through a point not on the line
_____ Copy an angle
_____ Parallel to a line through a point not on the line
E
F
G