Расчет прямоугольного треугольника с катетом a=20 и углом α°=15

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

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c = \(\frac{a}{\sin{α°}}\) = \(\frac{20}{\sin{(15°})}\) = \(\mathtt{\text{77.3}}\)

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β° = \(90°-α°\) = \(90°-15°\) = \(\mathtt{\text{75}}°\)

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h = \(a·\cos{α°}\) = \(20·\cos{(15°)}\) = \(\mathtt{\text{19.3}}\)

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b = \(\sqrt{c^2 - a^2}\) = \(\sqrt{\mathtt{\text{77.3}}^2-20^2}\) = \(\sqrt{5975.29-400}\) = \(\sqrt{5575.29}\) = \(\mathtt{\text{74.7}}\)b = \(h·\frac{c}{a}\) = \(\mathtt{\text{19.3}}·\frac{\mathtt{\text{77.3}}}{20}\) = \(\mathtt{\text{74.6}}\)b = \(c·\cos{α°}\) = \(\mathtt{\text{77.3}}·\cos{(15°)}\) = \(\mathtt{\text{74.7}}\)b = \(c·\sin{β°}\) = \(\mathtt{\text{77.3}}·\sin{(75°)}\) = \(\mathtt{\text{74.7}}\)b = \(\frac{h}{sin{α°}}\) = \(\frac{\mathtt{\text{19.3}}}{sin{(15°)}}\) = \(\mathtt{\text{74.6}}\)b = \(\frac{h}{sin{β°}}\) = \(\frac{\mathtt{\text{19.3}}}{sin{(75°)}}\) = \(\mathtt{\text{74.6}}\)b = \(\sqrt{\frac{c^2 - \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{77.3}}^2 - \sqrt{\mathtt{\text{77.3}}^4-4·\mathtt{\text{77.3}}^2·\mathtt{\text{19.3}}^2}}{2}}\) = \(\sqrt{\frac{5975.29-\sqrt{26801147.4957}}{2}}\) = \(\sqrt{399.0}\) = \(\mathtt{\text{20}}\)

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S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{19.3}}·\mathtt{\text{77.3}}}{2}\) = \(\mathtt{\text{746}}\)

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R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{77.3}}}{2}\) = \(\mathtt{\text{38.6}}\)

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mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{77.3}}}{2}\) = \(\mathtt{\text{38.6}}\)

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r = \(\frac{a+b-c}{2}\) = \(\frac{20+\mathtt{\text{74.6}}-\mathtt{\text{77.3}}}{2}\) = \(\mathtt{\text{8.65}}\)

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P = \(a+b+c\) = \(20+\mathtt{\text{74.6}}+\mathtt{\text{77.3}}\) = \(\mathtt{\text{172}}\)