Расчет прямоугольного треугольника с катетом b=4 и углом α°=3
Калькулятор прямоугольного треугольника — это инструмент, который помогает вычислять различные параметры прямоугольного треугольника, такие как длина сторон, площадь, периметр,углы и высоты.
Ответ:
\(a=\mathtt{\text{0.283}}\)
\(b=4\)
\(c=\mathtt{\text{4.01}}\)
\(3\)°
\(\mathtt{\text{87}}\)°
h=\(\mathtt{\text{0.209}}\)
mc=\(\mathtt{\text{2}}\)
Гипотенуза c:
c = \(\frac{b}{\cos{α°}}\) = \(\frac{4}{\cos{(3°})}\) = \(\mathtt{\text{4.01}}\)Угол β°:
β° = \(90°-α°\) = \(90°-3°\) = \(\mathtt{\text{87}}°\)Высота h:
h = \(b·\sin{α°}\) = \(4·\sin{(3°)}\) = \(\mathtt{\text{0.209}}\)Катет a:
a = \(\sqrt{c^2 - b^2}\) = \(\sqrt{\mathtt{\text{4.01}}^2 -4^2}\) = \(\sqrt{16.0801-16}\) = \(\sqrt{0.0800999999999981}\) = \(\mathtt{\text{0.283}}\)или:
a = \(h·\frac{c}{b}\) =\(\mathtt{\text{0.209}}·\frac{\mathtt{\text{4.01}}}{4}\) = \(\mathtt{\text{0.21}}\)или:
a = \(c·\sin{α°}\) = \(\mathtt{\text{4.01}}·\sin{(3°)}\) = \(\mathtt{\text{0.21}}\)или:
a = \(c·\cos{β°}\) = \(\mathtt{\text{4.01}}·\cos{(87°)}\) = \(\mathtt{\text{0.21}}\)или:
a = \(\frac{h}{cos{α°}}\) = \(\frac{\mathtt{\text{0.209}}}{cos{(3°)}}\) = \(\mathtt{\text{0.209}}\)или:
a = \(\frac{h}{sin{β°}}\) = \(\frac{(\mathtt{\text{0.209}})}{sin{(\mathtt{\text{87}}°)}}\) = \(\mathtt{\text{0.209}}\)или:
a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{4.01}}^2 + \sqrt{\mathtt{\text{4.01}}^4-4·\mathtt{\text{4.01}}^2·0.209^2}}{2}}\) = \(\sqrt{\frac{16.0801+\sqrt{255.7600366176}}{2}}\) = \(\sqrt{16.0}\) = \(\mathtt{\text{4}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{0.209}}·\mathtt{\text{4.01}}}{2}\) = \(\mathtt{\text{0.419}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{4.01}}}{2}\) = \(\mathtt{\text{2}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{4.01}}}{2}\) = \(\mathtt{\text{2}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{0.283}}+4-\mathtt{\text{4.01}}}{2}\) = \(\mathtt{\text{0.137}}\)Периметр P:
P = \(a+b+c\) = \(\mathtt{\text{0.283}}+4+\mathtt{\text{4.01}}\) = \(\mathtt{\text{8.29}}\)
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