Download Angles and Their Measure

Angles and Their Measure
I.
Basic Info;
a. Acute vs. Obtuse vs. Right
b. Complementary Angles: Two angles whose sum is ______.
c. Supplementary Angles:
Two angles whose sum is ______.
d. In a complete circle there are _______ degrees
II.
Degrees, Minutes, and Seconds
a. Each degree is split up into 60 parts, each part being 1/60 of a degree. These parts are
called __________.
b. Each minute is split up into 60 parts, each part being 1/60 of a minute (or 1/3600 of a
degree). These parts are called ___________.
c. Convert 25.42◦ to degrees, minutes, and seconds.
d. Convert 220◦15’35” to decimal form.
III.
Radian Measure
a. Two of the ways that we measure angles with are:
1) Degrees
(_____ parts to a rotation) used for triangle applications
2) Radians
(_____ parts to a rotation) used for circular applications
b. Recall from Geometry…
is the circumference of a circle divided by its
diameter
c. The circumference is about ___ times its diameter.
d. The Greeks named this number ____.
e. π ≈ _________
π ≈ _______
f. π is an _______________ number.
g.
It cannot be written as a terminating or repeating decimal.
h. The state of Indiana once tried to legislate π to exactly equal 22/7.
i.
What is a RADIAN?

Place an angle with the vertex at the center of a circle (this is called a
________________.

An angle measured in radians is the ratio of the ________________of the circle
to the _______________ of the circle.

FORMULAS:

Since the circumference of a circle is _______ , one complete rotation
would have arc length of _______.
j.

So θ = 1 rotation = _____° = ___ radians

So θ = ½ rotation = _____° = ___ radians

Conversion Factor:

30° can be converted to radians by…
Convert by hand:
30  _____ radians
45  _____ radians
60  _____ radians
315  _____ radians
120  _____ radians
k.
3
radians  _____ 
4

2
radians  _____ 
3
radians  _____ 
2
5
radians  _____ 
3
Convert using the calculator:
23  _____ radians
4 radians  _____ 
611  _____ radians
3.2 radians  _____ 
IV.
Arc Length
a. FORMULA:
b. Find, in centimeters, the length of an arc intercepted by a central angle of 4 radians in a
circle with a radius of 3.5 cm.
c. A sector has a radius of 12 cm. and an angle of 65º. To the nearest tenth of a cm., find
its arc length.
d. A person standing on the earth notices that a 747 Jumbo Jet
flying overhead subtends an angle of 0.45°. If the length of
the jet is 230 feet, find its altitude to the nearest thousand
feet.
V.
Area of a Sector of a Circle
a. FORMULA:
b. Find the area of the sector formed by a central angle of 1.4 radians in a circle of radius
2.1 meters.
c. A lawn sprinkler located at the corner of a yard is set to rotate through 90° and project
water out 30.0 feet. To three significant digits, what area of lawn is watered by the
sprinkler?