The rectangular triangle is made by two acute angles which size depends on lengths of the parties and also one corner always of invariable size 90 °. It is possible to calculate the size of an acute angle in degrees with use of trigonometrical functions or theorems of the sum of corners in triangle tops in Euclidean space.
Instruction
1. Use trigonometrical functions if in statements of the problem only sizes of the parties of a triangle are given. For example, on lengths of two legs (the short parties adjacent to a right angle) it is possible to calculate any of two acute angles. A tangent of that corner (β) which adjoins to a leg And, it can find division of length opposite the parties (a leg C) at length of the party And: tg(β) = V/A. And knowing a tangent, it is possible to calculate also the corner size corresponding to it in degrees. Function an arctangent is for this purpose intended: β = arctg (tg(β)) = arctg (V/A).
2. On the same formula it is possible to find size and other acute angle lying opposite to A. Prosto's leg change designations of the parties. But it is possible to make it and differently, by means of other couple of trigonometrical functions - a cotangent and an arc cotangent. The cotangent of a corner of b is defined by division of length of an adjacent leg And into length opposite In: tg(β) = And/VA will help to take an arc cotangent from the received value of size of a corner in degrees: β = arcctg (сtg(β)) = arcctg (A/V).
3. If in initial conditions length of one of legs (A) and a hypotenuse is given (C), then for calculation of corners use functions, the return to a sine and a cosine - an arcsine and an arccosine. The sine of an acute angle β is equal to the relation of length of the leg lying opposite to it In to hypotenuse length With: sin(β) = PREMIUM. Means, in degrees apply such formula to calculation of size of this corner: β = arcsin (V/S).
4. And the value of a cosine of the angle β is defined by the relation of length of the triangle of a leg adjoining this top And to length of a hypotenuse of S. Eto means that for calculation of size of a corner in degrees, by analogy with the previous formula, it is necessary to use such equality: β = arccos (And / C).
5. The theorem of the sum of corners of a triangle does unnecessary use of trigonometrical functions if in statements of the problem the size of one of acute angles is given. In this case for calculation of an unknown corner (α) just take away from 180 ° sizes of two known corners - direct (90 °) and sharp (β): α = 180 ° - 90 ° - β = 90 ° - β.