Download Arc Length With Angle Review Problem Set

Name: ________________________ Class: ___________________ Date: __________
ID: A
Trigonometry - Arc Length with Angle Review Problem Set
Short Answer
1. What is the radian measure of the smaller angle
formed by the hands of a clock at 7 o’clock?
5. Kristine is riding in car 4 of the Ferris wheel
represented in the accompanying diagram. The
Ferris wheel is rotating in the direction indicated by
the arrows. The eight cars are equally spaced
around the circular wheel. Express, in radians, the
measure of the smallest angle through which she
will travel to reach the bottom of the Ferris wheel.
2. Convert 3 radians to degrees and express the
answer to the nearest minute.
3. Express 260º in radian measure.
4. Express
3π
radians in degrees.
4
6. An arc of a circle that is 6 centimeters in length
intercepts a central angle of 1.5 radians. Find the
number of centimeters in the radius of the circle.
1
Name: ________________________
ID: A
12. In a circle, a central angle intercepts an arc of 12
centimeters. If the radius of the circle is 6
centimeters, find the number of radians in the
measure of the central angle.
7. Kathy and Tami are at point A on a circular track
that has a radius of 150 feet, as shown in the
accompanying diagram. They run
counterclockwise along the track from A to S, a
distance of 247 feet. Find, to the nearest degree,
the measure of minor arc AS.
13. An arc of a circle measures 30 centimeters and the
radius measures 10 centimeters. In radians, what is
the measure of the central angle that subtends the
arc?
14. In a circle whose radius is 2, a central angle
intercepts an arc whose length is 6. What is the
number of radians in the central angle of the arc?
8. The pendulum of a clock swings through an angle
of 2.5 radians as its tip travels through an arc of 50
centimeters. Find the length of the pendulum, in
centimeters.
1
radians at the center of a circle
4
intercepts an arc of 18 inches. Find the length of
the radius in inches.
15. An angle of 2
9. In a circle with a radius of 3 centimeters, find, in
centimeters, the length of an arc intercepted by a
central angle of 2 radians.
10. In a circle, an arc of length 10 is intercepted by a
2
central angle of radian. Find the radius of the
3
circle.
11. In a circle of radius 8, find the length of the arc
intercepted by a central angle of 1.5 radians.
2
ID: A
Trigonometry - Arc Length with Angle Review Problem Set
Answer Section
SHORT ANSWER
1. ANS:
5π
6
5
10π
5π
2π ⋅
=
=
12
6
12
PTS: 2
2. ANS:
3×
180
π
REF: 061125a2
STA: A2.M.1
TOP: Radian Measure
≈ 171.89° ≈ 171°53′ .
PTS: 2
KEY: degrees
3. ANS:
13π
9
REF: 011335a2
STA: A2.M.2
TOP: Radian Measure
PTS: 2
KEY: radians
4. ANS:
135
REF: 018401siii
STA: A2.M.2
TOP: Radian Measure
PTS: 2
KEY: degrees
5. ANS:
5π
.
4
REF: 018603siii
STA: A2.M.2
TOP: Radian Measure
PTS: 2
6. ANS:
REF: 010421b
STA: A2.M.1
TOP: Radian Measure
REF: 010526b
STA: A2.A.61
TOP: Arc Length
4.
PTS: 2
KEY: radius
1
ID: A
7. ANS:
94.
PTS: 4
KEY: angle
8. ANS:
.
.
REF: 060531b
STA: A2.A.61
TOP: Arc Length
REF: 060626b
STA: A2.A.61
TOP: Arc Length
PTS: 2
KEY: arc length
10. ANS:
15
REF: 068514siii
STA: A2.A.61
TOP: Arc Length
PTS: 2
KEY: radius
11. ANS:
12
REF: 068618siii
STA: A2.A.61
TOP: Arc Length
PTS: 2
KEY: arc length
12. ANS:
2
REF: 068713siii
STA: A2.A.61
TOP: Arc Length
PTS: 2
KEY: angle
13. ANS:
3
REF: 089508siii
STA: A2.A.61
TOP: Arc Length
PTS: 2
KEY: angle
14. ANS:
3
REF: 019615siii
STA: A2.A.61
TOP: Arc Length
PTS: 2
KEY: angle
15. ANS:
8
REF: 080108siii
STA: A2.A.61
TOP: Arc Length
PTS: 2
KEY: radius
REF: 060312siii
STA: A2.A.61
TOP: Arc Length
20.
PTS: 2
KEY: radius
9. ANS:
6
2