Triangle diagram for measuring heights of trees using proportions.

Using Proportions To Find Heights of Trees

Triangle diagram for measuring heights of trees using proportions.

Triangle diagram for measuring heights of trees using proportions

Using Proportions To Find Heights of Trees

Triangle diagram for measuring heights of trees using proportions

Parallelogram with angles labeled.

Parallelogram

Parallelogram with angles labeled.

Right angle with square at perpendicular lines

Right Angle

Right angle with square at perpendicular lines

Illustration of an angle

Angle

Illustration of an angle

Right angle at perpendicular lines demonstrated by string on plumb line.

Perpendicular Lines

Right angle at perpendicular lines demonstrated by string on plumb line.

Acute angle

Acute Angle

Acute angle

Obtuse angle

Obtuse Angle

Obtuse angle

Complementary angles

Complementary Angles

Complementary angles

Supplementary angles

Supplementary Angles

Supplementary angles

Right triangle with square

Right Triangle

Right triangle with square

Rectangle with angles labeled. Parallelogram with right angles.

Rectangle

Rectangle with angles labeled. Parallelogram with right angles.

Square with angles labeled. A rectangle with four equal sides.

Square

Square with angles labeled. A rectangle with four equal sides.

Trapezoid with angles and height labeled.

Trapezoid

Trapezoid with angles and height labeled.

Right triangle with squares that can be used to illustrate the Pythagorean Theorem.

Pythagorean Theorem Triangle

Right triangle with squares that can be used to illustrate the Pythagorean Theorem.

Illustration of steel square.

Steel Square

Illustration of steel square.

Illustration of steel square with hypotenuse drawn.

Steel Square

Illustration of steel square with hypotenuse drawn.

Illustration of steel square with bevel/slant.

Steel Square

Illustration of steel square with bevel/slant.

Square with diagonal and angles labeled.

Square

Square with diagonal and angles labeled.

Illustration of circle with inscribed angle and central angle.

Inscribed and Central Angles

Illustration of circle with inscribed angle and central angle.

Illustration of circle with inscribed angle 30 and central angle 60.

Inscribed and Central Angles 30 60

Illustration of circle with inscribed angle 30 and central angle 60.

Illustration of circle with sector and segment used to find area.

Circle With Sector and Segment labeled

Illustration of circle with sector and segment used to find area.

Illustration of partial circle with sector and segment used to find area.

Circle With Sector and Segment labeled

Illustration of partial circle with sector and segment used to find area.

Illustration of circle with radius of 4000, and triangle with 45 degree angle enclosed.

Circles With Radius 4000 and Enclosed Triangle

Illustration of circle with radius of 4000, and triangle with 45 degree angle enclosed.

Illustration of circle with quadrant and 60 degree arc.

Quadrant of Circle With 60 degree Arc

Illustration of circle with quadrant and 60 degree arc.

Illustration of construction to lay off an angle.

Construction of Angle

Illustration of construction to lay off an angle.

An illustration of a right circular cone with altitude of 10 ft. and angle of 30 degrees.

Right Circular Cone 10 Feet High With 30 Degree Angle

An illustration of a right circular cone with altitude of 10 ft. and angle of 30 degrees.

Positive trigonometric angle with initial and terminal sides labeled.

Positive Trigonometric Angle

Positive trigonometric angle with initial and terminal sides labeled.

Negative trigonometric angle with initial and terminal sides labeled.

Negative Trigonometric Angle

Negative trigonometric angle with initial and terminal sides labeled.

Trigonometric angle 467 degrees.

467 Degree Trigonometric Angle

Trigonometric angle 467 degrees.

Trigonometric angle -229 degrees.

-229 Degree Trigonometric Angle

Trigonometric angle -229 degrees.

Axes showing trigonometric angles, and quadrants.

Trigonometric Angles and Quadrants

Axes showing trigonometric angles, and quadrants.

Illustration showing that the radian is an angle that when placed at the center of a circle its sides intercept an arc equal to the radius.

Radians in Complete Circle

Illustration showing that the radian is an angle that when placed at the center of a circle its sides…

Illustration showing that the arc length can be found by multiplying the angle measure by the radius of the circle.

Model of Arc Length, Angle Measure, and Radius

Illustration showing that the arc length can be found by multiplying the angle measure by the radius…

Illustration of acute angle theta as part of a right triangle.

Acute Angle Theta

Illustration of acute angle theta as part of a right triangle.

Lines drawn to horizontal to form triangle ratios (reference triangles, angles).

Reference Angles/Triangles Formed by Angles in Quadrants

Lines drawn to horizontal to form triangle ratios (reference triangles, angles).

Lines drawn to horizontal to form triangle ratios (reference triangles, angles). Axes, quadrants, abscissa, ordinate, and distance labeled.

Reference Angles/Triangles Formed by Angles in Quadrants With Labels

Lines drawn to horizontal to form triangle ratios (reference triangles, angles). Axes, quadrants, abscissa,…

Right triangle OQP with angle of 40 degrees, height of .64 inches, and hypotenuse of 1 inch.

Right Triangle With Sides .64 and 1 and Angle of 40 degrees

Right triangle OQP with angle of 40 degrees, height of .64 inches, and hypotenuse of 1 inch.

Right triangle OQP with angle of 35 degrees, height of .70 inches, and leg of 1 inch.

Right Triangle With Sides .7 and 1 and Angle of 35 degrees

Right triangle OQP with angle of 35 degrees, height of .70 inches, and leg of 1 inch.

Special right triangle with angles 45 degrees, 45 degrees, and 90 degrees with side measures/relationships shown.

Special Right Triangle with Angles 45, 45, 90 degrees

Special right triangle with angles 45 degrees, 45 degrees, and 90 degrees with side measures/relationships…

Special right triangle with angles 30 degrees, 60 degrees, and 90 degrees with side measures/relationships shown.

Special Right Triangle with Angles 30, 60, 90 degrees

Special right triangle with angles 30 degrees, 60 degrees, and 90 degrees with side measures/relationships…

Trigonometric reference triangles/angles drawn for 60 degree reference angel in quadrants I and II.

Trigonometric Reference Triangles/Angles (60 degrees) Drawn in Quadrants

Trigonometric reference triangles/angles drawn for 60 degree reference angel in quadrants I and II.

Trigonometric reference triangles/angles drawn for reference angel in quadrants I and II. This illustration could be used to find trig ratios.

Trigonometric Reference Triangles/Angles Drawn in Quadrants

Trigonometric reference triangles/angles drawn for reference angel in quadrants I and II. This illustration…

Inclined plane forming right triangle showing the velocity of a body sliding a distance,s, down a smooth horizontal plane.

Inclined Plane Forming Right Triangle

Inclined plane forming right triangle showing the velocity of a body sliding a distance,s, down a smooth…

Illustration modeling the path of a projectile.

Path of Projectile

Illustration modeling the path of a projectile.

Illustration modeling the illumination on a surface when the surface is not perpendicular to hte rays of light from a source of light.

Illumination of a Surface When the Surface is not Perpendicular to the Source

Illustration modeling the illumination on a surface when the surface is not perpendicular to hte rays…

Right triangle ABC with a base angle of 67 degrees 4208 minutes and a hypotenuse of 23.47 ft.

Right Triangle ABC With Angle 67 degrees 42.8 minutes and Hypotenuse 23.47 ft.

Right triangle ABC with a base angle of 67 degrees 4208 minutes and a hypotenuse of 23.47 ft.

Right triangle ABC with a leg of 23.85 feet and a hypotenuse of 35.62 feet.

Right Triangle ABC With Leg 23.85 ft. and Hypotenuse 35.62 ft.

Right triangle ABC with a leg of 23.85 feet and a hypotenuse of 35.62 feet.

A perpendicular line drawn from point P to straight line RS.

Perpendicular Line Drawn From Point P to Line RS

A perpendicular line drawn from point P to straight line RS.

CD is the projection of AB upon OX. In each case AE=CD and AE=ABcos theta.

Projection of a Line Segment

CD is the projection of AB upon OX. In each case AE=CD and AE=ABcos theta.

OP is a line representing a vector (directed quantity)

Vector

OP is a line representing a vector (directed quantity)

OP is a vector (directed quantity) showing the force by a weight acting on it at an angle of 20 degrees.

Vector Showing Force at Angle of 20 degrees

OP is a vector (directed quantity) showing the force by a weight acting on it at an angle of 20 degrees.

Illustration showing an angle of elevation from a horizontal line to a line of sight.

Angle of Elevation

Illustration showing an angle of elevation from a horizontal line to a line of sight.

Illustration showing an angle of depression from a horizontal line to a line of sight.

Angle of Depression

Illustration showing an angle of depression from a horizontal line to a line of sight.

Illustration showing an angle of 23 degrees 40 minutes making a triangle in a city block and marking off streets at 100 foot intervals.

Triangular City Block With Angles and Lengths

Illustration showing an angle of 23 degrees 40 minutes making a triangle in a city block and marking…

Illustration showing a survey on the lake front in Chicago with distances and angle measures shown.

Survey of Lake Front in Chicago

Illustration showing a survey on the lake front in Chicago with distances and angle measures shown.

Illustration showing a circle inscribed in a regular pentagon. Or, a regular pentagon circumscribed about a circle.

Regular Pentagon With Circle Inscribed

Illustration showing a circle inscribed in a regular pentagon. Or, a regular pentagon circumscribed…

Right triangle ABC with angles A, B, C to be used for finding distance across a river. This is a trigonometry problem. Wishing to determine the width of the river, I observed a tree standing directly across on the bank. The angle of elevation of the top of the tree was 32 degrees. At 150 ft. back from this point and in the same direction from the tree the angle of elevation of the top of the tree was 21 degrees. Find the width of the river.

Right Triangle For Finding Distance Across a River

Right triangle ABC with angles A, B, C to be used for finding distance across a river. This is a trigonometry…

Circle with 36 degree angles marked. This diagram can be used with the following trig problem: Locate the centers of the holes B and C by finding the distance each is to the right and above the center O. The radius of the circle is 1.5 inches. Compute correct to three decimal places.

Circle With 36 degree Angles and Radius 1.5 in.

Circle with 36 degree angles marked. This diagram can be used with the following trig problem: Locate…

Circle with chord AB=2 ft. and radius OA = 3 ft.. Triangle AOC is a right triangle. Angle AOC=half angle AOB, and the central angle AOB has the same measure as the arc AnB.

Circle With a Chord of 2 ft. and a Radius of 3 ft.

Circle with chord AB=2 ft. and radius OA = 3 ft.. Triangle AOC is a right triangle. Angle AOC=half angle…