Расчет прямоугольного треугольника с катетом b=465 и углом α°=9
Калькулятор прямоугольного треугольника — это инструмент, который помогает вычислять различные параметры прямоугольного треугольника, такие как длина сторон, площадь, периметр,углы и высоты.
Ответ:
\(a=\mathtt{\text{74.9}}\)
\(b=465\)
\(c=\mathtt{\text{471}}\)
\(9\)°
\(\mathtt{\text{81}}\)°
h=\(\mathtt{\text{72.7}}\)
mc=\(\mathtt{\text{236}}\)
Гипотенуза c:
c = \(\frac{b}{\cos{α°}}\) = \(\frac{465}{\cos{(9°})}\) = \(\mathtt{\text{471}}\)Угол β°:
β° = \(90°-α°\) = \(90°-9°\) = \(\mathtt{\text{81}}°\)Высота h:
h = \(b·\sin{α°}\) = \(465·\sin{(9°)}\) = \(\mathtt{\text{72.7}}\)Катет a:
a = \(\sqrt{c^2 - b^2}\) = \(\sqrt{\mathtt{\text{471}}^2 -465^2}\) = \(\sqrt{221841-216225}\) = \(\sqrt{5616}\) = \(\mathtt{\text{74.9}}\)или:
a = \(h·\frac{c}{b}\) =\(\mathtt{\text{72.7}}·\frac{\mathtt{\text{471}}}{465}\) = \(\mathtt{\text{73.6}}\)или:
a = \(c·\sin{α°}\) = \(\mathtt{\text{471}}·\sin{(9°)}\) = \(\mathtt{\text{73.7}}\)или:
a = \(c·\cos{β°}\) = \(\mathtt{\text{471}}·\cos{(81°)}\) = \(\mathtt{\text{73.7}}\)или:
a = \(\frac{h}{cos{α°}}\) = \(\frac{\mathtt{\text{72.7}}}{cos{(9°)}}\) = \(\mathtt{\text{73.6}}\)или:
a = \(\frac{h}{sin{β°}}\) = \(\frac{(\mathtt{\text{72.7}})}{sin{(\mathtt{\text{81}}°)}}\) = \(\mathtt{\text{73.6}}\)или:
a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{471}}^2 + \sqrt{\mathtt{\text{471}}^4-4·\mathtt{\text{471}}^2·72.7^2}}{2}}\) = \(\sqrt{\frac{221841+\sqrt{44523453205.44}}{2}}\) = \(\sqrt{2.16 \cdot 10^{5}}\) = \(\mathtt{\text{465}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{72.7}}·\mathtt{\text{471}}}{2}\) = \(\mathtt{\text{1.71e+04}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{471}}}{2}\) = \(\mathtt{\text{236}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{471}}}{2}\) = \(\mathtt{\text{236}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{74.9}}+465-\mathtt{\text{471}}}{2}\) = \(\mathtt{\text{34.4}}\)Периметр P:
P = \(a+b+c\) = \(\mathtt{\text{74.9}}+465+\mathtt{\text{471}}\) = \(\mathtt{\text{1.01e+03}}\)
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