Расчет прямоугольного треугольника с катетом b=5 и углом α°=20 и углом β°=70
Калькулятор прямоугольного треугольника — это инструмент, который помогает вычислять различные параметры прямоугольного треугольника, такие как длина сторон, площадь, периметр,углы и высоты.
Ответ:
\(a=\mathtt{\text{1.82}}\)
\(b=5\)
\(c=\mathtt{\text{5.32}}\)
\(20\)°
\(70\)°
h=\(\mathtt{\text{1.71}}\)
mc=\(\mathtt{\text{2.66}}\)
Гипотенуза c:
c = \(\frac{b}{\sin{β°}}\) = \(\frac{5}{\sin{(70°})}\) = \(\mathtt{\text{5.32}}\)или:
c = \(\frac{b}{\cos{α°}}\) = \(\frac{5}{\cos{(20°})}\) = \(\mathtt{\text{5.32}}\)Высота h:
h = \(b·\sin{α°}\) = \(5·\sin{(20°)}\) = \(\mathtt{\text{1.71}}\)или:
h = \(b·\cos{β°}\) = \(5·\cos{(70°)}\) = \(\mathtt{\text{1.71}}\)Катет a:
a = \(\sqrt{c^2 - b^2}\) = \(\sqrt{\mathtt{\text{5.32}}^2 -5^2}\) = \(\sqrt{28.3024-25}\) = \(\sqrt{3.3024}\) = \(\mathtt{\text{1.82}}\)или:
a = \(h·\frac{c}{b}\) =\(\mathtt{\text{1.71}}·\frac{\mathtt{\text{5.32}}}{5}\) = \(\mathtt{\text{1.82}}\)или:
a = \(c·\sin{α°}\) = \(\mathtt{\text{5.32}}·\sin{(20°)}\) = \(\mathtt{\text{1.82}}\)или:
a = \(c·\cos{β°}\) = \(\mathtt{\text{5.32}}·\cos{(70°)}\) = \(\mathtt{\text{1.82}}\)или:
a = \(\frac{h}{cos{α°}}\) = \(\frac{\mathtt{\text{1.71}}}{cos{(20°)}}\) = \(\mathtt{\text{1.82}}\)или:
a = \(\frac{h}{sin{β°}}\) = \(\frac{(\mathtt{\text{1.71}})}{sin{(70°)}}\) = \(\mathtt{\text{1.82}}\)или:
a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{5.32}}^2 + \sqrt{\mathtt{\text{5.32}}^4-4·\mathtt{\text{5.32}}^2·1.71^2}}{2}}\) = \(\sqrt{\frac{28.3024+\sqrt{469.9896544}}{2}}\) = \(\sqrt{25.0}\) = \(\mathtt{\text{5}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{1.71}}·\mathtt{\text{5.32}}}{2}\) = \(\mathtt{\text{4.55}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{5.32}}}{2}\) = \(\mathtt{\text{2.66}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{5.32}}}{2}\) = \(\mathtt{\text{2.66}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{1.82}}+5-\mathtt{\text{5.32}}}{2}\) = \(\mathtt{\text{0.75}}\)Периметр P:
P = \(a+b+c\) = \(\mathtt{\text{1.82}}+5+\mathtt{\text{5.32}}\) = \(\mathtt{\text{12.1}}\)
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