Расчет прямоугольного треугольника с катетом b=0.6 и углом β°=55
Калькулятор прямоугольного треугольника — это инструмент, который помогает вычислять различные параметры прямоугольного треугольника, такие как длина сторон, площадь, периметр,углы и высоты.
Ответ:
\(a=\mathtt{\text{0.419}}\)
\(b=0.6\)
\(c=\mathtt{\text{0.732}}\)
\(\mathtt{\text{35}}\)°
\(55\)°
h=\(\mathtt{\text{0.344}}\)
mc=\(\mathtt{\text{0.366}}\)
Гипотенуза c:
c = \(\frac{b}{\sin{β°}}\) = \(\frac{0.6}{\sin{(55°})}\) = \(\mathtt{\text{0.732}}\)Угол α°:
α° = \(90°-β°\) = \(90°-55°\) = \(\mathtt{\text{35}}°\)Высота h:
h = \(b·\cos{β°}\) = \(0.6·\cos{(55°)}\) = \(\mathtt{\text{0.344}}\)Катет a:
a = \(\sqrt{c^2 - b^2}\) = \(\sqrt{\mathtt{\text{0.732}}^2 -0.6^2}\) = \(\sqrt{0.535824-0.36}\) = \(\sqrt{0.175824}\) = \(\mathtt{\text{0.419}}\)или:
a = \(h·\frac{c}{b}\) =\(\mathtt{\text{0.344}}·\frac{\mathtt{\text{0.732}}}{0.6}\) = \(\mathtt{\text{0.42}}\)или:
a = \(c·\sin{α°}\) = \(\mathtt{\text{0.732}}·\sin{(35°)}\) = \(\mathtt{\text{0.42}}\)или:
a = \(c·\cos{β°}\) = \(\mathtt{\text{0.732}}·\cos{(55°)}\) = \(\mathtt{\text{0.42}}\)или:
a = \(\frac{h}{cos{α°}}\) = \(\frac{\mathtt{\text{0.344}}}{cos{(35°)}}\) = \(\mathtt{\text{0.42}}\)или:
a = \(\frac{h}{sin{β°}}\) = \(\frac{(\mathtt{\text{0.344}})}{sin{(55°)}}\) = \(\mathtt{\text{0.42}}\)или:
a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{0.732}}^2 + \sqrt{\mathtt{\text{0.732}}^4-4·\mathtt{\text{0.732}}^2·0.344^2}}{2}}\) = \(\sqrt{\frac{0.535824+\sqrt{0.03347828352}}{2}}\) = \(\sqrt{0.359}\) = \(\mathtt{\text{0.599}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{0.344}}·\mathtt{\text{0.732}}}{2}\) = \(\mathtt{\text{0.126}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{0.732}}}{2}\) = \(\mathtt{\text{0.366}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{0.732}}}{2}\) = \(\mathtt{\text{0.366}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{0.419}}+0.6-\mathtt{\text{0.732}}}{2}\) = \(\mathtt{\text{0.143}}\)Периметр P:
P = \(a+b+c\) = \(\mathtt{\text{0.419}}+0.6+\mathtt{\text{0.732}}\) = \(\mathtt{\text{1.75}}\)
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