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 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.

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

An isosceles triangle with angles 2, 89, 89

Isosceles Triangle degrees 2, 89, 89

An isosceles triangle with angles 2, 89, 89

An isosceles triangle with angles 3, 88.5, 88.5

Isosceles Triangle degrees 3, 88.5, 88.5

An isosceles triangle with angles 3, 88.5, 88.5

An isosceles triangle with angles 4, 88, 88

Isosceles Triangle degrees 4, 88, 88

An isosceles triangle with angles 4, 88, 88

An isosceles triangle with angles 5, 87.5, 87.5

Isosceles Triangle degrees 5, 87.5, 87.5

An isosceles triangle with angles 5, 87.5, 87.5

An isosceles triangle with angles 6, 87, 87

Isosceles Triangle degrees 6, 87, 87

An isosceles triangle with angles 6, 87, 87

An isosceles triangle with angles 7, 86.5, 86.5

Isosceles Triangle degrees 7, 86.5, 86.5

An isosceles triangle with angles 7, 86.5, 86.5

An isosceles triangle with angles 8, 86, 86

Isosceles Triangle degrees 8, 86, 86

An isosceles triangle with angles 8, 86, 86

An isosceles triangle with angles 9, 85.5, 85.5

Isosceles Triangle degrees 9, 85.5, 85.5

An isosceles triangle with angles 9, 85.5, 85.5

An isosceles triangle with angles 10, 85, 85

Isosceles Triangle degrees 10, 85, 85

An isosceles triangle with angles 10, 85, 85

An isosceles triangle with angles 11, 84.5, 84.5

Isosceles Triangle degrees 11, 84.5, 84.5

An isosceles triangle with angles 11, 84.5, 84.5

An isosceles triangle with angles 12, 84, 84

Isosceles Triangle degrees 12, 84, 84

An isosceles triangle with angles 12, 84, 84

An isosceles triangle with angles 13, 83.5, 83.5

Isosceles Triangle degrees 13, 83.5, 83.5

An isosceles triangle with angles 13, 83.5, 83.5

An isosceles triangle with angles 14, 83, 83

Isosceles Triangle degrees 14, 83, 83

An isosceles triangle with angles 14, 83, 83

An isosceles triangle with angles 15, 82.5, 82.5

Isosceles Triangle degrees 15, 82.5, 82.5

An isosceles triangle with angles 15, 82.5, 82.5

An isosceles triangle with angles 16, 82, 82

Isosceles Triangle degrees 16, 82, 82

An isosceles triangle with angles 16, 82, 82

An isosceles triangle with angles 17, 81.5, 81.5

Isosceles Triangle degrees 17, 81.5, 81.5

An isosceles triangle with angles 17, 81.5, 81.5

An isosceles triangle with angles 18, 81, 81

Isosceles Triangle degrees 18, 81, 81

An isosceles triangle with angles 18, 81, 81

An isosceles triangle with angles 19, 80.5, 80.5

Isosceles Triangle degrees 19, 80.5, 80.5

An isosceles triangle with angles 19, 80.5, 80.5

An isosceles triangle with angles 20, 80, 80

Isosceles Triangle degrees 20, 80, 80

An isosceles triangle with angles 20, 80, 80

An isosceles triangle with angles 21, 79.5, 79.5

Isosceles Triangle degrees 21, 79.5, 79.5

An isosceles triangle with angles 21, 79.5, 79.5

An isosceles triangle with angles 22, 79, 79

Isosceles Triangle degrees 22, 79, 79

An isosceles triangle with angles 22, 79, 79

An isosceles triangle with angles 23, 78.5, 78.5

Isosceles Triangle degrees 23, 78.5, 78.5

An isosceles triangle with angles 23, 78.5, 78.5