Расчет прямоугольного треугольника с гипотенузой c=12 и высотой h=3

Калькулятор прямоугольного треугольника — это инструмент, который помогает вычислять различные параметры прямоугольного треугольника, такие как длина сторон, площадь, периметр,углы и высоты.

---

a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{12^2 + \sqrt{12^4-4·12^2·3^2}}{2}}\) = \(\sqrt{\frac{144+\sqrt{15552}}{2}}\) = \(\sqrt{134.0}\) = \(\mathtt{\text{11.6}}\)

---

b = \(\sqrt{\frac{c^2 - \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{12^2 - \sqrt{12^4-4·12^2·3^2}}{2}}\) = \(\sqrt{\frac{144-\sqrt{15552}}{2}}\) = \(\sqrt{9.65}\) = \(\mathtt{\text{3.11}}\)

---

S = \(\frac{hc}{2}\) = \(\frac{3·12}{2}\) = \(\mathtt{\text{18}}\)

---

R = \(\frac{c}{2}\) = \(\frac{12}{2}\) = \(\mathtt{\text{6}}\)

---

mc = \(\frac{c}{2}\) = \(\frac{12}{2}\) = \(\mathtt{\text{6}}\)

---

α° = \(\arcsin{\frac{a}{c}}\) = \(\arcsin{\frac{\mathtt{\text{11.6}}}{12}}\) = \(\arcsin({0.97})\) = \(\mathtt{\text{75.2}}°\)

---

β° =\(\arccos{\frac{a}{c}}\) = \(\arccos{\frac{\mathtt{\text{11.6}}}{12}}\) = \(\arccos({0.97})\) = \(\mathtt{\text{14.8}}°\)

---

r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{11.6}}+\mathtt{\text{3.11}}-12}{2}\) = \(\mathtt{\text{1.35}}\)

---

P = \(a+b+c\) = \(\mathtt{\text{11.6}}+\mathtt{\text{3.11}}+12\) = \(\mathtt{\text{26.7}}\)