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A right triangle is a geometric figure with a right angle. There are two kinds of right-angled triangles: ordinary right-angled triangles and isosceles right-angled triangles. It conforms to Pythagorean theorem and has some special properties and judgment methods.
The first method can be called "equal diameter method"
The Arabic mathematician and astronomer Nasir Ear Nail (13rd century) and the German mathematician Rejomontanus (15th century) first adopted the term equal diameter method.
"The sine of the two internal angles of a triangle is regarded as a sine line in a circle with the same radius (16th century ago, the trigonometric function was regarded as a line segment rather than a ratio), and the ratio of the two is equal to the ratio of the opposite sides of the angle by using the similar triangles property.
Nasir Din extends to the opposite sides of two internal angles at the same time, and the structural radius is larger than the circles on both sides. Reggiomontanus simplified Nasir al-Din's method, and only extended the shorter of the two sides to construct a circle with the same radius as the longer one. From 17 to 18, China mathematician and astronomer Mei Wending and British mathematician Simpson independently simplified the "equal diameter method".
/kloc-At the beginning of the 0/8th century, "equal diameter method" evolved into "right triangle method". This method does not need to select and calculate the radius of the circle, but only needs to calculate the height line of the triangle, and the sine theorem can be obtained by using the angular relationship of the right triangle. 19th century, the British mathematician Woodhouse began to uniformly take R= 1, which is equivalent to expressing trigonometric functions by ratios, and obtained the "height method" widely used today.
The second method is the "circumscribed circle method", which was first adopted by the French mathematician Veda in the16th century. David did not discuss the obtuse triangle, which was supplemented by later mathematicians.
References:
Baidu encyclopedia-sine theorem Baidu encyclopedia-Pythagorean theorem