Расчет прямоугольного треугольника с катетом b=6 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:
\(a=\mathtt{\text{3.47}}\)
\(b=6\)
\(c=\mathtt{\text{6.93}}\)
\(30\)°
\(60\)°
h=\(\mathtt{\text{3}}\)
mc=\(\mathtt{\text{3.46}}\)
Гипотенуза c:
c = \(\frac{b}{\sin{β°}}\) = \(\frac{6}{\sin{(60°})}\) = \(\mathtt{\text{6.93}}\)или:
c = \(\frac{b}{\cos{α°}}\) = \(\frac{6}{\cos{(30°})}\) = \(\mathtt{\text{6.93}}\)Высота h:
h = \(b·\sin{α°}\) = \(6·\sin{(30°)}\) = \(\mathtt{\text{3}}\)или:
h = \(b·\cos{β°}\) = \(6·\cos{(60°)}\) = \(\mathtt{\text{3}}\)Катет a:
a = \(\sqrt{c^2 - b^2}\) = \(\sqrt{\mathtt{\text{6.93}}^2 -6^2}\) = \(\sqrt{48.0249-36}\) = \(\sqrt{12.0249}\) = \(\mathtt{\text{3.47}}\)или:
a = \(h·\frac{c}{b}\) =\(\mathtt{\text{3}}·\frac{\mathtt{\text{6.93}}}{6}\) = \(\mathtt{\text{3.46}}\)или:
a = \(c·\sin{α°}\) = \(\mathtt{\text{6.93}}·\sin{(30°)}\) = \(\mathtt{\text{3.46}}\)или:
a = \(c·\cos{β°}\) = \(\mathtt{\text{6.93}}·\cos{(60°)}\) = \(\mathtt{\text{3.46}}\)или:
a = \(\frac{h}{cos{α°}}\) = \(\frac{\mathtt{\text{3}}}{cos{(30°)}}\) = \(\mathtt{\text{3.46}}\)или:
a = \(\frac{h}{sin{β°}}\) = \(\frac{(\mathtt{\text{3}})}{sin{(60°)}}\) = \(\mathtt{\text{3.46}}\)или:
a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{6.93}}^2 + \sqrt{\mathtt{\text{6.93}}^4-4·\mathtt{\text{6.93}}^2·3^2}}{2}}\) = \(\sqrt{\frac{48.0249+\sqrt{577.49462001}}{2}}\) = \(\sqrt{36.0}\) = \(\mathtt{\text{6}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{3}}·\mathtt{\text{6.93}}}{2}\) = \(\mathtt{\text{10.4}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{6.93}}}{2}\) = \(\mathtt{\text{3.46}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{6.93}}}{2}\) = \(\mathtt{\text{3.46}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{3.47}}+6-\mathtt{\text{6.93}}}{2}\) = \(\mathtt{\text{1.27}}\)Периметр P:
P = \(a+b+c\) = \(\mathtt{\text{3.47}}+6+\mathtt{\text{6.93}}\) = \(\mathtt{\text{16.4}}\)
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