Depending on the particular task, you can find side isosceles triangle , if given base any additional element.
base and height to nemu.Perpendikulyar conducted to the base of an isosceles triangle , is simultaneously high, median and bisector of the opposite angle.This interesting feature can use, using the Pythagorean theorem: a = √ (h² + (c / 2) ²), where a - length of the equal sides of the triangle , h - height, held to the base.
base and the height of one of the side storon.Provedya height to the side, you get two right triangles .The hypotenuse of one of them - the unknown side of the isosceles triangle , leg - defined height h.The second leg is unknown, his x mark.
Consider a second right-angled triangle.Its hypotenuse - base total figure, one of
the legs is equal to h.The other leg is the difference a - x.By the Pythagorean theorem write two equations for the unknowns a and x: a² = x² + h²; c² = (a - x) ² + h².
Let base is 10, and the height of 8, then: a² = x² + 64; 100 = (a - x) ² + 64.
Express artificiallyintroduced the variable x from the second equation and substitute it at first: a - x = 6 → x = a - 6a² = (a - 6) ² + a = 64 → 25/3.
base and one of the equal angles α.Provedite height to the base, consider one of the right-angled triangles.The cosine of the tilt angle is the ratio of the adjacent side to the hypotenuse.In this case, the leg is equal to half the base of an isosceles triangle , and the hypotenuse - its side: (c / 2) / a = cos α → a = c / (2 • cos α).
base and the opposite corner β.Opustite perpendicular to the base .The angle of the resulting single-angled triangles is equal to β / 2.The sine of the angle is the ratio of the opposite leg to the hypotenuse and where: a = c / (2 • sin (β / 2))