Angle of degree 178

Angle Degrees 178

Angle of degree 178

Angle of degree 179

Angle Degrees 179

Angle of degree 179

"...let us suppose the object a, to be placed before the mirror, and nearer to it than the principal focus. Then the rays proceeding from the extremities of the object without interruption, would continue to diverge in the lines o and n, as seen behind the mirror' but by reflection they are made to diverge less than before, and consequently to make the angle under which the meet more obtuse at the eye b, than it would be if they continued onward to e, where they would have met without reflection. The result therefore, is to render the image h, upon the eye, as much larger than the object a, as the angle at the eye is more obtuse than the angle at e." -Comstock 1850

Object Within the Focus in a Concave Mirror

"...let us suppose the object a, to be placed before the mirror, and nearer to it than the principal…

"Suppose the object a, appears to the naked eye of the length repreesnted in the drawing. Now, as the rays coming from each end of the object, form by their convergence at the eye, the visual angle, or the angle under which the object is seem, and we call objects large or small in proportion as this angle is obtuse or acute, if, therefore, the object a be withdrawn futher from the eye, it is apparent that the rays o, o, proceeding from its extremities, will enter the eye under a more acute angle, and therefore that the object will appear diminished in proportion." -Comstock 1850

Visual Angle

"Suppose the object a, appears to the naked eye of the length repreesnted in the drawing. Now, as the…

Inclined plane using right triangle and proportions

Inclined Plane Triangle

Inclined plane using right triangle and 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.

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

Obtuse angle

Obtuse Angle

Obtuse angle

Triangle, triangular polygon

Triangular Polygon

Triangle, triangular polygon

Right triangle with square

Right Triangle

Right triangle with square

Triangle with medians drawn.

Triangle with Medians

Triangle with medians drawn.

Parallelogram illustration to show where the area of a triangle formula comes from.

Area of Triangle

Parallelogram illustration to show where the area of a triangle formula comes from.

Triangle with dimensions labeled. Triangle can be used to calculate area.

Triangle With Dimensions

Triangle with dimensions labeled. Triangle can be used to calculate area.

Triangle with dimensions labeled. Triangle can be used to calculate area.

Triangle With Dimensions

Triangle with dimensions labeled. Triangle can be used to calculate area.

Pentagon with dimensions labeled. Pentagon can be used to calculate area by calculating individual triangles and finding the sum of the areas.

Pentagon With Triangular Sections For Area

Pentagon with dimensions labeled. Pentagon can be used to calculate area by calculating individual triangles…

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

Triangle

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

Triangle with sides labeled with numerals 28, 36, 40 and angles A, B, C labeled.

Triangle 28, 36, 40

Triangle with sides labeled with numerals 28, 36, 40 and angles A, B, C 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.

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

Right Triangle ABC

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

Triangle with labels A, B, C, D

Triangle

Triangle with labels A, B, C, D

Similar triangles with corresponding sides labeled.

Similar Triangles

Similar triangles with corresponding sides labeled.

Similar triangles with corresponding sides labeled.

Similar Triangles

Similar triangles with corresponding sides labeled.

Illustration of similar triangles used to find distance across a stream

Similar Triangles for Distance Across Stream

Illustration of similar triangles used to find distance across a stream

Illustration of similar triangles used to find distance across a lake.

Similar Triangles for Distance Across Lake

Illustration of similar triangles used to find distance across a lake.

Illustration of similar triangles used to find height of smokestack.

Similar Triangles for Height of Smokestack

Illustration of similar triangles used to find height of smokestack.

Illustration of roof and rafter with rise and run to show pitch.

Pitch of Roof

Illustration of roof and rafter with rise and run to show pitch.

Sketch of isosceles triangle with labels.

Isosceles Triangle

Sketch of isosceles triangle with labels.

Square with diagonal and angles labeled.

Square

Square with diagonal and angles labeled.

Sketch of equilateral triangle with bisectors, medians, and altitudes.

Equilateral Triangle

Sketch of equilateral triangle with bisectors, medians, and altitudes.

30-60-90 Right Triangle

Triangle 30-60-90

30-60-90 Right Triangle

Regular hexagon with equilateral triangles divided in the interior.

Regular Hexagon

Regular hexagon with equilateral triangles divided in the interior.

Steam pipe illustration of 30-60-90 triangle.

Triangle Steam Pipe

Steam pipe illustration of 30-60-90 triangle.

30-60-90 right triangle.

30-60-90 Right Triangle

30-60-90 right triangle.

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…