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.

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.

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…

Illustration showing the diameter of a circle inscribed in a right triangle is equal to the difference between the sum of the legs and the hypotenuse.

Circle Inscribed in a Right Triangle

Illustration showing the diameter of a circle inscribed in a right triangle is equal to the difference…

Illustration of a circle with a right angle inscribed in a semicircle.

Circle With Inscribed Right Angle in Semicircle

Illustration of a circle with a right angle inscribed in a semicircle.

Illustration where one leg of a right triangle is the diameter of a circle. The tangent at the point where the circumference cuts the hypotenuse bisects the other leg.

Circle With a Right Triangle

Illustration where one leg of a right triangle is the diameter of a circle. The tangent at the point…

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=- 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…

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…

Draftsman's third method for drawing an ellipse

Ellipse Third Method

Draftsman's third method for drawing an ellipse

A flashcard featuring an illustration of a Right Triangle

Flashcard of a Right Triangle

A flashcard featuring an illustration of a Right Triangle

Showing different types of forms or shapes: rectangle, right triangle, acute triangle, and obtuse triangle.

Forms

Showing different types of forms or shapes: rectangle, right triangle, acute triangle, and obtuse triangle.

Illustration used to prove the Pythagorean Theorem, according to Euclid. A perpendicular is drawn from the top vertex of the right triangle extended through the bottom square, forming 2 rectangles. Each rectangle has the same area as one of the two legs. This proves that the sum of the squares of the legs is equal to the square of the hypotenuse (Pythagorean Theorem).

Euclid's Pythagorean Theorem Proof

Illustration used to prove the Pythagorean Theorem, according to Euclid. A perpendicular is drawn from…

Illustration that can be used to prove the Pythagorean Theorem, the sum of the squares of the legs is equal to the square of the hypotenuse.

Geometric Pythagorean Theorem Proof

Illustration that can be used to prove the Pythagorean Theorem, the sum of the squares of the legs is…

Illustration that can be used to prove the Pythagorean Theorem, the sum of the squares of the legs is equal to the square of the hypotenuse. The geometrical illustration depicts a 3,4,5 right triangle with the square units drawn to prove that the sum of the squares of the legs (9 + 16) equals the square of the hypotenuse.

Geometric Pythagorean Theorem Proof

Illustration that can be used to prove the Pythagorean Theorem, the sum of the squares of the legs is…

A visual illustration used to prove the Pythagorean Theorem by rearrangement. When the 4 identical triangles are removed, the areas are equal. Thus, proving the sum of the squares of the legs is equal to the square of the hypotenuse.

Pythagorean Theorem Proof by Rearrangement

A visual illustration used to prove the Pythagorean Theorem by rearrangement. When the 4 identical triangles…

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…

"In any right triangle, the square described on the hypotenuse is equal to the sum of the squares described on the other two sides. If A B C, is a right triangle, right angled at B, then the square described on the hypotenuse AC is equal to the sum of the suares described on the sides A B and B C." — Hallock, 1905

Right Triangle

"In any right triangle, the square described on the hypotenuse is equal to the sum of the squares described…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a right triangle.

Right Triangle

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a right triangle.

Right Triangle

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a right triangle.

Right Triangle

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures consisting of triangles, squares, and parallelograms are used to construct the given shape. This tangram depicts a right triangle.

Right Triangle

Tangrams, invented by the Chinese, are used to develop geometric thinking and spatial sense. Seven figures…

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…

Illustration used to show "If one acute angle of a right triangle is double the other, the hypotenuse is double the shorter side."

Relationships In A Right Triangle

Illustration used to show "If one acute angle of a right triangle is double the other, the hypotenuse…

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.…

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…

An illustration of a right triangle inscribed in a semicircle.

Right Triangle Inscribed In A Semicircle

An illustration of a right triangle inscribed in a semicircle.

Four different types of forms or shapes: right triangle, isosceles triangle, rectangle, and circle.

Shapes

Four different types of forms or shapes: right triangle, isosceles triangle, rectangle, and circle.

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…

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

Right triangle with angle of 25 ° 33' 7" and side of 37' 7"

Triangle With Angle of 25 ° 33' 7" and Side of 37' 7"

Right triangle with angle of 25 ° 33' 7" and side of 37' 7"

Right triangle with angle of 29 ° 31' and side of 24.

Triangle With Angle of 29 ° 31' and Side of 24

Right triangle with angle of 29 ° 31' and side of 24.

Inclined plane using right triangle and proportions

Inclined Plane Triangle

Inclined plane using right triangle and proportions

Right triangle inscribed in semicircle. Illustration shows that the perpendicular from any point in the circumference to the diameter of a circle is the mean proportional between the segments of the diameter.

Right Triangle Inscribed in Semicircle Shows Mean Proportional

Right triangle inscribed in semicircle. Illustration shows that the perpendicular from any point in…

An isosceles triangle with angles 90, 45, 45

Isosceles Triangle degrees 90, 45, 45

An isosceles triangle with angles 90, 45, 45

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.

Illustration of a right triangle used to show the Pythagorean Theorem (the square of the hypotenuse is equal to the sum of the squares of the legs).

Right Triangle

Illustration of a right triangle used to show the Pythagorean Theorem (the square of the hypotenuse…

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 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 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…

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 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.

Illustration of a right triangle that can be used to show Pythagorean theorem. "In any right triangle, the square described upon the hypotenuse is equal to the sum of the squares described upon the other two sides."

Right Triangle Showing Pythagorean Theorem

Illustration of a right triangle that can be used to show Pythagorean theorem. "In any right triangle,…

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.

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 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.

Right triangle with side .024967 and hypotenuse .04792.

Right Triangle With Side .024967 and Hypotenuse .04792

Right triangle with side .024967 and hypotenuse .04792.

Right triangle with side 234 and hypotenuse 308.

Right Triangle With Side 234 and Hypotenuse 308

Right triangle with side 234 and hypotenuse 308.

Right triangle with sides 15 and 18.

Right Triangle With Sides 15 and 18

Right triangle with sides 15 and 18.

Illustration of a right triangle with legs labeled 150 and 85. This could be used to find the hypotenuse using Pythagorean Theorem.

Right Triangle With Sides 85 and 150

Illustration of a right triangle with legs labeled 150 and 85. This could be used to find the hypotenuse…