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The square root of 2 is equal to the length of the hypotenuse of a right triangle with legs of length 1 and is therefore a constructible number. In geometry and algebra, a real number is constructible if and only if, given a line segment of unit length, a line segment of length | | can be constructed with compass and straightedge in a finite number of steps.
A square is a tool used for marking and referencing a 90° angle, though mitre squares are used for 45° angles. Squares see common use in woodworking, metalworking, construction and technical drawing. [1] Some squares incorporate a scale for measuring distances (a ruler) or for calculating angles.
A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle in which one full rotation is 360 degrees. [4] It is not an SI unit—the SI unit of angular measure is the radian—but it is mentioned in the SI brochure as an accepted unit. [5]
Angle trisection is the construction, using only a straightedge and a compass, of an angle that is one-third of a given arbitrary angle. This is impossible in the general case. For example, the angle 2 π /5 radians (72° = 360°/5) can be trisected, but the angle of π /3 radians (60°) cannot be trisected. [8]
A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. For example, a right triangle may have angles that form simple relationships, such as 45°–45°–90°. This is called an "angle-based" right triangle.
The example shows trisection of any angle θ > 3π / 4 by a ruler with length equal to the radius of the circle, giving trisected angle φ = θ / 3 . Angle trisection is a classical problem of straightedge and compass construction of ancient Greek mathematics.
The S, T, and ST scales are used for trig functions and multiples of trig functions, for angles in degrees. For angles from around 5.7 up to 90 degrees, sines are found by comparing the S scale with C (or D) scale. (On many closed-body rules the S scale relates to the A and B scales instead and covers angles from around 0.57 up to 90 degrees ...
One could say, "The Moon's diameter subtends an angle of half a degree." The small-angle formula can convert such an angular measurement into a distance/size ratio. Other astronomical approximations include: 0.5° is the approximate diameter of the Sun and of the Moon as viewed from Earth. 1° is the approximate width of the little finger at ...