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The values of sine and cosine of 30 and 60 degrees are derived by analysis of the equilateral triangle. In an equilateral triangle, the 3 angles are equal and sum to 180°, therefore each corner angle is 60°. Bisecting one corner, the special right triangle with angles 30-60-90 is obtained.
When each equatorial degree was divided into 18 leagues, the geographical mile was equal to 1 / 54 degree or about 2.06 kilometres (1.28 mi); when divided into 20 leagues, the geographical mile was equal to 1 / 60 degree, approximating the values provided above; and when divided into 25 leagues, the geographical mile was equal ...
A geographical mile is defined to be the length of one minute of arc along the equator (one equatorial minute of longitude) therefore a degree of longitude along the equator is exactly 60 geographical miles or 111.3 kilometers, as there are 60 minutes in a degree. The length of 1 minute of longitude along the equator is 1 geographical mile or 1 ...
In mathematics, sine and cosine are trigonometric functions of an angle.The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that ...
Since predicted or reported wind speeds are rarely accurate, corrections to the aircraft's heading need to be made at regular intervals. Skinny triangles form the basis of the 1 in 60 rule, which is "After travelling 60 miles, your heading is one degree off for every mile you're off course". "60" is very close to 180 / π = 57.30.
If units of degrees are intended, the degree sign must be explicitly shown (sin x°, cos x°, etc.). Using this standard notation, the argument x for the trigonometric functions satisfies the relationship x = (180 x / π )°, so that, for example, sin π = sin 180° when we take x = π .
degrees and decimal minutes: 40° 26.767′ N 79° 58.933′ W; decimal degrees: +40.446 -79.982; There are 60 minutes in a degree and 60 seconds in a minute. Therefore, to convert from a degrees minutes seconds format to a decimal degrees format, one may use the formula
The 60th parallel north is a circle of latitude that is 60 degrees north of Earth's equator. It crosses Europe , Asia , the Pacific Ocean , North America , and the Atlantic Ocean . Although it lies approximately twice as far away from the Equator as from the North Pole , the 60th parallel is half as long as the Equator line, due to the cosine ...