Расчет прямоугольного треугольника с катетом a=25 и углом α°=70 и углом β°=20
Калькулятор прямоугольного треугольника — это инструмент, который помогает вычислять различные параметры прямоугольного треугольника, такие как длина сторон, площадь, периметр,углы и высоты.
Ответ:
\(a=25\)
\(b=\mathtt{\text{9.1}}\)
\(c=\mathtt{\text{26.6}}\)
\(70\)°
\(20\)°
h=\(\mathtt{\text{8.55}}\)
mc=\(\mathtt{\text{13.3}}\)
Гипотенуза c:
c = \(\frac{a}{\cos{β°}}\) = \(\frac{25}{\cos{(20°})}\) = \(\mathtt{\text{26.6}}\)или:
c = \(\frac{a}{\sin{α°}}\) = \(\frac{25}{\sin{(70°})}\) = \(\mathtt{\text{26.6}}\)Высота h:
h = \(a·\cos{α°}\) = \(25·\cos{(70°)}\) = \(\mathtt{\text{8.55}}\)или:
h = \(a·\sin{β°}\) = \(25·\sin{(20°)}\) = \(\mathtt{\text{8.55}}\)Катет b:
b = \(\sqrt{c^2 - a^2}\) = \(\sqrt{\mathtt{\text{26.6}}^2-25^2}\) = \(\sqrt{707.56-625}\) = \(\sqrt{82.5600000000001}\) = \(\mathtt{\text{9.09}}\)или:
b = \(h·\frac{c}{a}\) = \(\mathtt{\text{8.55}}·\frac{\mathtt{\text{26.6}}}{25}\) = \(\mathtt{\text{9.1}}\)или:
b = \(c·\cos{α°}\) = \(\mathtt{\text{26.6}}·\cos{(70°)}\) = \(\mathtt{\text{9.1}}\)или:
b = \(c·\sin{β°}\) = \(\mathtt{\text{26.6}}·\sin{(20°)}\) = \(\mathtt{\text{9.1}}\)или:
b = \(\frac{h}{sin{α°}}\) = \(\frac{\mathtt{\text{8.55}}}{sin{(70°)}}\) = \(\mathtt{\text{9.1}}\)или:
b = \(\frac{h}{sin{β°}}\) = \(\frac{\mathtt{\text{8.55}}}{sin{(20°)}}\) = \(\mathtt{\text{9.1}}\)или:
b = \(\sqrt{\frac{c^2 - \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{26.6}}^2 - \sqrt{\mathtt{\text{26.6}}^4-4·\mathtt{\text{26.6}}^2·\mathtt{\text{8.55}}^2}}{2}}\) = \(\sqrt{\frac{707.56-\sqrt{293743.534}}{2}}\) = \(\sqrt{82.8}\) = \(\mathtt{\text{9.1}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{8.55}}·\mathtt{\text{26.6}}}{2}\) = \(\mathtt{\text{114}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{26.6}}}{2}\) = \(\mathtt{\text{13.3}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{26.6}}}{2}\) = \(\mathtt{\text{13.3}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{25+\mathtt{\text{9.1}}-\mathtt{\text{26.6}}}{2}\) = \(\mathtt{\text{3.75}}\)Периметр P:
P = \(a+b+c\) = \(25+\mathtt{\text{9.1}}+\mathtt{\text{26.6}}\) = \(\mathtt{\text{60.7}}\)
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