Расчет прямоугольного треугольника с катетом b=8 и углом α°=30 и углом β°=60
Калькулятор прямоугольного треугольника — это инструмент, который помогает вычислять различные параметры прямоугольного треугольника, такие как длина сторон, площадь, периметр,углы и высоты.
Ответ:
\(a=\mathtt{\text{4.62}}\)
\(b=8\)
\(c=\mathtt{\text{9.24}}\)
\(30\)°
\(60\)°
h=\(\mathtt{\text{4}}\)
mc=\(\mathtt{\text{4.62}}\)
Гипотенуза c:
c = \(\frac{b}{\sin{β°}}\) = \(\frac{8}{\sin{(60°})}\) = \(\mathtt{\text{9.24}}\)или:
c = \(\frac{b}{\cos{α°}}\) = \(\frac{8}{\cos{(30°})}\) = \(\mathtt{\text{9.24}}\)Высота h:
h = \(b·\sin{α°}\) = \(8·\sin{(30°)}\) = \(\mathtt{\text{4}}\)или:
h = \(b·\cos{β°}\) = \(8·\cos{(60°)}\) = \(\mathtt{\text{4}}\)Катет a:
a = \(\sqrt{c^2 - b^2}\) = \(\sqrt{\mathtt{\text{9.24}}^2 -8^2}\) = \(\sqrt{85.3776-64}\) = \(\sqrt{21.3776}\) = \(\mathtt{\text{4.62}}\)или:
a = \(h·\frac{c}{b}\) =\(\mathtt{\text{4}}·\frac{\mathtt{\text{9.24}}}{8}\) = \(\mathtt{\text{4.62}}\)или:
a = \(c·\sin{α°}\) = \(\mathtt{\text{9.24}}·\sin{(30°)}\) = \(\mathtt{\text{4.62}}\)или:
a = \(c·\cos{β°}\) = \(\mathtt{\text{9.24}}·\cos{(60°)}\) = \(\mathtt{\text{4.62}}\)или:
a = \(\frac{h}{cos{α°}}\) = \(\frac{\mathtt{\text{4}}}{cos{(30°)}}\) = \(\mathtt{\text{4.62}}\)или:
a = \(\frac{h}{sin{β°}}\) = \(\frac{(\mathtt{\text{4}})}{sin{(60°)}}\) = \(\mathtt{\text{4.62}}\)или:
a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{9.24}}^2 + \sqrt{\mathtt{\text{9.24}}^4-4·\mathtt{\text{9.24}}^2·4^2}}{2}}\) = \(\sqrt{\frac{85.3776+\sqrt{1825.16818176}}{2}}\) = \(\sqrt{64.0}\) = \(\mathtt{\text{8}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{4}}·\mathtt{\text{9.24}}}{2}\) = \(\mathtt{\text{18.5}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{9.24}}}{2}\) = \(\mathtt{\text{4.62}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{9.24}}}{2}\) = \(\mathtt{\text{4.62}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{4.62}}+8-\mathtt{\text{9.24}}}{2}\) = \(\mathtt{\text{1.69}}\)Периметр P:
P = \(a+b+c\) = \(\mathtt{\text{4.62}}+8+\mathtt{\text{9.24}}\) = \(\mathtt{\text{21.9}}\)
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