Illustration used to prove "Two angles whose sides are perpendicular each to each are either equal or…

Illustration used to prove "An exterior angle of a triangle is equal to the sum of the two remote interior…

Illustration used to prove "If the sides of any polygon are prolonged in succession one way, no two…

Illustration used to prove "The sum of all the angles of any polygon is twice as many right angles as…

A 6 inches diameter protractor to measure angles to half degrees, made of brass or German silver. They…

Illustration showing that the volume of 2 triangular pyramids, having the same trihedral angle of the…

Illustration of an angle &alpha with the vertex at the center, O, of a circle with radius OB. AC and…

Illustration of an angle &alpha with the terminal side used to draw a triangle in quadrant I.

Illustration of an angle with the terminal side used to draw a triangle in quadrant II.

A detached triangular work in fortification, with two embankments which form a projecting angle. In…

In field fortification, the simplest kind of work employed, consisting of two parapets of earth raised…

"The angle, ABD, included between the direction of the moving body before it strikes the reflecting…

"... if a ball be thrown from F against the surface B C so as to strike it perpendicularly at A, it…

"The ray a, c, is the ray of incidence, and that from c, to d, is the ray or reflection. The angles…

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

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

A propeller airplane with rudder, elevator, and ailerons. The rudder stabilizes the plane vertical,…

A secant is "a line which cuts a figure in any way. Specifically, in trigonometry, a line from the center…

"Nautically, a block with two sheaves, whose axes are at right angles to each other, used for the buntlines…

Illustration two types of triangles that can be used to model the law of sines. "In a plane triangle…

Illustration of a right spherical triangle and the five circular parts placed in the sectors of a circle…

Illustration used, with the law of sines, to find the relation between two sides of a spherical triangle…

Illustration used, with the law of cosines, to find the relation between the three sides and an angle…

Illustration used to extend the law of cosines when finding the relation between the three sides and…

Illustration used to extend the law of cosines when finding the relation between the three sides and…

Illustration of a right spherical triangle with a and b the sides, and α and β the angles…

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

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

"An instrument for the measurement of horizontal angles, consisting essentially of a telescope mounted…

"An instrument much employed in land-surveying for the measurement of angles horizontal and verticle."…

Triangle diagram for measuring heights of trees using proportions.

Triangle diagram for measuring heights of trees using proportions

Illustration used to construct a triangle given the length of the base and the two base angles.

Illustration showing an acute triangle (one that has all three angles that are acute).

Illustration to show altitudes drawn from base angles of an isosceles triangle.

Illustration used to prove "The bisectors of the angles of a triangle are concurrent in a point which…

Illustration to show that the bisector of an exterior angle of an isosceles triangle, formed by producing…

Illustration to show perpendicular bisectors in a triangle. It is known as the circumcenter.

Illustration showing an equiangular triangle (one that has all three angles that are equal).

An illustration showing a triangle with interior angles A, B, C, and exterior angles D, and A' + B'.

Illustration showing a triangle with exterior angles. This can be used to show the sum of the three…

Illustration to show angle bisectors in a triangle. It is known as the incenter.