Geometry Unit 10 Study Guide

Common angle measurements in rad and degrees

0° = 0 rad 15° = π/12 rad 30° = π/6 rad 45° = π/4 rad 60° = π/3 rad 75° = 5π/12 rad 90° = π/2 rad 180° = π rad 270° = 3π/2 rad 360° = 2π rad

The process known as solving a _____ is used for calculating unknown side lengths or angle measures of a triangle if certain of the side lengths and/or angle measures are known. a. triangle b. parallelogram c. square d. rectangle

a. triangle

An angle in standard position is an angle with its vertex at the origin and one of its rays on the ___ of the coordinate plane. a. x-axis b. y-axis c. intersection d. vertex

a. x-axis

___ ratios are the ratios of the lengths of the two sides of a right triangle. a. Algebraic b. Similar c. Trigonometric d. Geometric

c. Trigonometric

Convert from radians to degrees. 3 rad = _____ a. 229.2° b. 143.2° c. 180° d. 172° e. 85.9°

d. 172°

Convert from radians to degrees. 0.4 rad = _____ a. 143.2° b. 85.9° c. 180° d. 23° e. 229.2°

d. 23°

Angle of elevation is the angle formed by a horizontal line and a line of sight to a point _____ the horizon. a. below b. on c. near d. above

d. above

Angle of depression is the angle formed by a horizontal line and a line of sight to a point _____ the horizon. a. near b. above c. on d. below

d. below

The ___ is a trigonometric ratio consisting of the length of the hypotenuse to the length of the side opposite a given angle of a right triangle a. secant b. tangent c. sine d. cosecant

d. cosecant

The ___ is a trigonometric ratio consisting of the length of the side adjacent to a given acute angle of a right triangle to the length of side opposite the given angle. a. tangent b. cosine c. sine d. cotangent

d. cotangent

The branch of mathematics that deals with the relationships between sides and angles of triangles is called _____. a. geometry b. math models c. algebra d. trigonometry

d. trigonometry

Convert from degrees to radians. 55°= _____ rad a. 36π/11 b. 55π c. 55/180 d. 180π e. 11π/36

e. 11π/36

Convert from radians to degrees. 0.6 rad = _____ a. 85.9° b. 229.2° c. 143.2° d. 180° e. 34°

e. 34°

Convert from degrees to radians. 25° = _____ rad a. 180π b. 36π/5 c. 25/180 d. 25π e. 5π/36

e. 5π/36

Rad conversion and degree conversion

rad to degrees: xrad(180/π) degrees to rad: xdegrees(π/180)

Law of Sine, 2 angles 1 side

sinA sinB sinC ---- = ---- = ---- a b c

How to find the rad of a circle

C 2πr - = --- r r

SOHCAHTOA

Sine Opposite Hypotenuse Cosine Adjacent Hypotenuse Tangent Opposite Adjacent

Convert from degrees to radians. 120° = _____ rad a. 2π/3 b. 3π/2 c. 120π d. 23 e. 120

a. 2π/3

Convert from degrees to radians. 150°= _____ rad a. 5π/6 b. 6π/5 c. 150 d. 150π e. 5/6

a. 5π/6

_____ is the branch of mathematics that deals with the relationships between the sides and angles of triangles. a. Trigonometry b. Geometry c. Calculus d. Algebra

a. Trigonometry

The positive nth root of the product of n factors is the _____. a. geometric mean b. geometric ratio c. arithmetic mean d. trig factor

a. geometric mean

Angle of ___ is the angle formed by a horizontal line and line of sight to a point above the horizon. a. inclusion b. depression c. elevation d. sight

c. elevation

If you know the lengths of two sides and the measure of _____ angle(s) of a right triangle, you can find the measure of the other two angles and the length of the other side. a. one b. similar c. two d. concurrent

a. one

A radian is a unit of angular measure equal to the length of the arc divided by the ___ of the arc. a. radius b. diameter c. length d. degree

a. radius

The positive acute angle formed by the terminal side of an angle in standard position and the x-axis is called a ___ angle. a. reference b. standard c. terminal d. radial

a. reference

The reciprocal of the cosine is the ___. a. secant b. cosecant c. sine d. tangent

a. secant

Which trigonometric ratio is calculated by opposite/adjacent ? a. tangent b. cosecant c. sine d. cotangent e. cosine

a. tangent

The process of calculating unknown side lengths or angle measures of a triangle if certain of the side lengths and/or angle measures are known is known as solving a _____. a. triangle b. polygon c. square d. problem

a. triangle

If you know the lengths of _____ and the measure of one angle of a right triangle, you can find the measure of the other two angles and the length of the other side. a. two sides b. two vertices c. one side d. one altitude

a. two sides

Law of Cosine, 2 sides 1 angle

a²=b²+c²-2bc cosA b²=a²+c²-2ac cosB c²=a²+b²-2ab cosC

Convert from radians to degrees. 6 rad = _____ a. 229.2° b. 344° c. 85.9° d. 143.2° e. 180°

b. 344°

The positive _____ angle formed by the terminal side of an angle in standard position and the x-axis is called a reference angle. a. obtuse b. acute c. terminal d. right

b. acute

If you know the length of all three sides of a right triangle, you can find the measure of each of the three _____. a. transversals b. angles c. altitudes d. vertices

b. angles

If you know the measure of two _____ and the length of one side of a triangle, you can find the measure of the other angle and the length of the other two sides. a. sides b. angles c. altitudes d. vertices

b. angles

The three expressions, sin-1, cos-1, and tan-1 are called _____ trigonometric functions. a. transverse b. inverse c. converse d. reverse

b. inverse

A unit circle is a circle with a radius of ___ unit(s) that has its center at the origin on the coordinate plane. a. two b. one c. four d. three

b. one

A _____ is a unit of angular measure equal to the length of the arc divided by the radius of the arc. a. radical b. radian c. degree d. terminus

b. radian

The ratios of the lengths of the two sides of a right triangle are called ___ ratios. a. congruent b. trigonometric c. similar d. geometric

b. trigonometric

If you know the measure of two _____ and the length of one side of a right triangle, you can find the measure of the other angle and the length of the other two sides. a. vertices b. altitudes c. angles d. interiors

c. angles

The _____ is useful for finding the average of a set of values that are similar. a. geometric mean b. trigonometric mean c. arithmetic mean d. algebraic mean

c. arithmetic mean

If you know the lengths of all three _____ of a right triangle, you can find the measures of each of the three angles. a. perimeters b. altitudes c. sides d. areas

c. sides

Which trigonometric ratio is calculated by opposite/hypotenuse? a. cosecant b. cosine c. sine d. tangent e. cotangent

c. sine

The terminal side of an angle is the ray of the angle in standard position that does not lie on the _____. a. y-axis b. angle c. x-axis d. plane

c. x-axis

Convert from degrees to radians. 20°= _____ rad a. 180π b. 9π c. π/9 d. 1/9 e. 20π

c. π/9