Illustration of three circles enclosed in an equilateral triangle.

Circles Enclosed in Equilateral Triangle

Illustration of three circles enclosed in an equilateral triangle.

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 gothic arch about equilateral triangle.

Gothic Arch

Illustration of gothic arch about equilateral triangle.

Illustration of triangle inscribed in circle. Or, circle circumscribed about triangle.

Triangle Inscribed in Circle

Illustration of triangle inscribed in circle. Or, circle circumscribed about triangle.

37-49-94 Triangle

Triangle 37-49-94

37-49-94 Triangle

Triangle construction when given two angles and the included side.

Triangle Construction When Given 2 Angles and Included Side

Triangle construction when given two angles and the included side.

Illustration of a figure made up of 4 smaller figures (triangles).

Composite Figure

Illustration of a figure made up of 4 smaller figures (triangles).

Illustration of regular hexagon and triangle inscribed in circle.

Hexagon Inscribed in Circle by Construction

Illustration of regular hexagon and triangle inscribed in circle.

Prism with triangular bases.

Right Triangular Prism

Prism with triangular bases.

An illustration of a pyramid with a triangular base.

Pyramid With Triangular Base

An illustration of a pyramid with a triangular base.

An illustration of a prismatoid with triangular faces and points labeled.

Prismatoid With Triangular Faces

An illustration of a prismatoid with triangular faces and points labeled.

An illustration of a pyramid with the top cut off by a plane parallel to the base. The remaining part is called a frustum. This frustum has right triangular bases, one with 20 inch side and the other with a 30 inch side. Height is 27 inches.

Pyramid Frustum With Triangular Bases and Height of 27 inches

An illustration of a pyramid with the top cut off by a plane parallel to the base. The remaining part…

An illustration of a pyramid with the top cut off by a plane parallel to the base. The remaining part is called a frustum. This frustum has triangular bases with 14 inch sides. The other sides are 16 and 22 inches. The altitude is 24 inches.

Pyramid Frustum With Triangular Bases and Height of 27 inches

An illustration of a pyramid with the top cut off by a plane parallel to the base. The remaining part…

An illustration of a right triangle made up of a flagpole, rope, and the ground. Illustration could be used with Pythagorean Theorem.

Right Triangle Formed by Flagpole (x feet high) and Ground With Rope (x+4 feet)

An illustration of a right triangle made up of a flagpole, rope, and the ground. Illustration could…

An illustration of a right triangle with sides, 40, 75, and x. Additional height of x is added to 75. Illustration could be used with Pythagorean theorem.

Right Triangle With Sides x, 75, and 40

An illustration of a right triangle with sides, 40, 75, and x. Additional height of x is added to 75.…

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 ABC with sides a, b, c and angles A, B, C labeled.

Right Triangle ABC

Right triangle ABC with sides a, b, c and angles A, B, C labeled.

Right triangle ABC with sides a, b, c and angles A, B, C labeled.

Right Triangle ABC

Right triangle ABC with sides a, b, c and angles A, B, C labeled.

Right triangle ABC with sides m,n, p and angles A, B, C labeled.

Right Triangle ABC

Right triangle ABC with sides m,n, p and angles A, B, C labeled.

Right triangle ABC with angles A, B, C labeled.

Right Triangle ABC

Right triangle ABC with angles A, B, C labeled.

Right triangle ABC with angles A, B, C labeled and sides of length 3,4, and 5

Right Triangle 3,4,5

Right triangle ABC with angles A, B, C labeled and sides of length 3,4, and 5

Right triangle ABC with angles A, B, C labeled and leg of 13 with hypotenuse of 15.

Right Triangle with leg 13 and hypotenuse 15

Right triangle ABC with angles A, B, C labeled and leg of 13 with hypotenuse of 15.

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…

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.

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.

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…

Roof with a slope of 30 degrees. Angle theta is the inclination to the horizontal of the line AB, drawn in the roof and making an angle of 35 degrees with the line of greatest slope.

Roof With 30 degree Inclination for Trigonometry Triangle Problems

Roof with a slope of 30 degrees. Angle theta is the inclination to the horizontal of the line AB, drawn…

Two set squares, whose sides are 3,4, and 5 in., are placed so that their 4-in. sides and right angles coincide, and the angle between the 3-in. sides is 50 degrees. Theta, Ǝ is the angle between the longest sides.

Two Squares With Sides of Lengths 3,4,5 Placed at Right Angles to Each Other

Two set squares, whose sides are 3,4, and 5 in., are placed so that their 4-in. sides and right angles…

Circle modeling the earth. O is the center of the earth, r the radius of the earth, and h the height of the point P above the surface; it is required to find the distance from the point P to the horizon at A.

Circle With Center o and Radius r with point P

Circle modeling the earth. O is the center of the earth, r the radius of the earth, and h the height…

Illustration of blueprint used by highway engineers to widen the pavement on the inside of the curve of a road.

Curve in Pavement of Road

Illustration of blueprint used by highway engineers to widen the pavement on the inside of the curve…

Coordinate axis with angle XOP equal to theta, Θ, and angle XOQ=180 - Θ. From any point in the terminal side of XOP, as B, a perpendicular can be drawn, AB, to the x-axis; and from D, any point in the terminal side o f XOQ, perpendicular CD can be drawn to the x-axis. The right triangles OAB and OCD are similar. Also, OA, AB, OB, CD, and OD are positive, while OC is negative.

Coordinate Axis With Angles, Lines, and Perpendiculars Drawn

Coordinate axis with angle XOP equal to theta, Θ, and angle XOQ=180 - Θ. From any point in the terminal…

Angle XOP=Θ and angle XOQ=90+Θ. From a point in the terminal side of each a perpendicular line is drawn to the x-axis. The right triangles AOB and OCD thus formed are similar, and have all their sides positive except OC

Coordinate Axis With Perpendiculars Drawn To Form Similar Right Triangles

Angle XOP=Θ and angle XOQ=90+Θ. From a point in the terminal side of each a perpendicular line is…

Angle XOP=Θ and angle XOQ=- Θ. From a point in the terminal side of each a perpendicular line is drawn to the x-axis. The right triangles OAB and OAC thus formed are similar, and have all their sides positive except AC, which is negative.

Coordinate Axis With Perpendiculars Drawn To Form Similar Right Triangles From Positive and Negative Theta, Θ

Angle XOP=Θ and angle XOQ=- Θ. From a point in the terminal side of each a perpendicular line is drawn…

Right triangle OCB that can be used to show the relationships between x, y, r, and Θ.

Right Triangle OCB With, x, y, and r shown

Right triangle OCB that can be used to show the relationships between x, y, r, and Θ.

Angles used to illustrate the sum and difference of two angles and trig identities.

Angles Used to Illustrate Sum and Difference of Two Angles

Angles used to illustrate the sum and difference of two angles and trig identities.

Triangle ABC with sides a,b,c labeled and angles A,B,C labeled and h labeled as height.

Triangle ABC With Height h

Triangle ABC with sides a,b,c labeled and angles A,B,C labeled and h labeled as height.

Triangle ABC with sides a,b,c labeled and angles A,B,C labeled and h labeled as height.

Obtuse Triangle ABC With Height h

Triangle ABC with sides a,b,c labeled and angles A,B,C labeled and h labeled as height.

Obtuse triangle ABC with sides a,b,c labeled and angles A,B,C labeled.

Obtuse Triangle ABC

Obtuse triangle ABC with sides a,b,c labeled and angles A,B,C labeled.

Triangle ABC and triangle ABC'. This illustration could be used to demonstrate the law of sines.

Triangles ABC and ABC'

Triangle ABC and triangle ABC'. This illustration could be used to demonstrate the law of sines.

Illustration showing ambiguous case when the solution is not a triangle using law of sines.

Ambiguous Case of Law of Sines Triangle

Illustration showing ambiguous case when the solution is not a triangle using law of sines.

Illustration of oblique triangle used to find distance across a lake.

Oblique Triangle for Distance Across Lake

Illustration of oblique triangle used to find distance across a lake.

Illustration of oblique triangle used to find distance across a river.

Oblique Triangle for Distance Across a River

Illustration of oblique triangle used to find distance across a river.

Illustration of oblique triangle used to find distance across a river.

Oblique Triangle for Distance Across a River

Illustration of oblique triangle used to find distance across a river.

Illustration of the resultant vector when two vectors are acting upon a body at point P.

Resultant Vectors

Illustration of the resultant vector when two vectors are acting upon a body at point P.

Illustration of the resultant vector when four vectors are acting upon a body at point P.

Resultant Vector From 4 Forces

Illustration of the resultant vector when four vectors are acting upon a body at point P.

Illustration of the resultant vector when two vectors are acting upon a body at point P at 90 degrees.

Resultant Vector With Vectors at 90 degrees

Illustration of the resultant vector when two vectors are acting upon a body at point P at 90 degrees.

Illustration of the resultant vector when two vectors are acting upon a body at point P at Ǝ degrees.

Resultant Vector With Vectors at Angle Ǝ

Illustration of the resultant vector when two vectors are acting upon a body at point P at Ǝ degrees.

An isosceles triangle with angles 1, 89.5, 89.5

Isosceles Triangle degrees 1, 89.5, 89.5

An isosceles triangle with angles 1, 89.5, 89.5