Расчет прямоугольного треугольника с катетом b=0.6 и углом β°=2
Калькулятор прямоугольного треугольника — это инструмент, который помогает вычислять различные параметры прямоугольного треугольника, такие как длина сторон, площадь, периметр,углы и высоты.
Ответ:
\(a=\mathtt{\text{17.2}}\)
\(b=0.6\)
\(c=\mathtt{\text{17.2}}\)
\(\mathtt{\text{88}}\)°
\(2\)°
h=\(\mathtt{\text{0.6}}\)
mc=\(\mathtt{\text{8.6}}\)
Гипотенуза c:
c = \(\frac{b}{\sin{β°}}\) = \(\frac{0.6}{\sin{(2°})}\) = \(\mathtt{\text{17.2}}\)Угол α°:
α° = \(90°-β°\) = \(90°-2°\) = \(\mathtt{\text{88}}°\)Высота h:
h = \(b·\cos{β°}\) = \(0.6·\cos{(2°)}\) = \(\mathtt{\text{0.6}}\)Катет a:
a = \(\sqrt{c^2 - b^2}\) = \(\sqrt{\mathtt{\text{17.2}}^2 -0.6^2}\) = \(\sqrt{295.84-0.36}\) = \(\sqrt{295.48}\) = \(\mathtt{\text{17.2}}\)или:
a = \(h·\frac{c}{b}\) =\(\mathtt{\text{0.6}}·\frac{\mathtt{\text{17.2}}}{0.6}\) = \(\mathtt{\text{17.2}}\)или:
a = \(c·\sin{α°}\) = \(\mathtt{\text{17.2}}·\sin{(88°)}\) = \(\mathtt{\text{17.2}}\)или:
a = \(c·\cos{β°}\) = \(\mathtt{\text{17.2}}·\cos{(2°)}\) = \(\mathtt{\text{17.2}}\)или:
a = \(\frac{h}{cos{α°}}\) = \(\frac{\mathtt{\text{0.6}}}{cos{(88°)}}\) = \(\mathtt{\text{17.2}}\)или:
a = \(\frac{h}{sin{β°}}\) = \(\frac{(\mathtt{\text{0.6}})}{sin{(2°)}}\) = \(\mathtt{\text{17.2}}\)или:
a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{17.2}}^2 + \sqrt{\mathtt{\text{17.2}}^4-4·\mathtt{\text{17.2}}^2·0.6^2}}{2}}\) = \(\sqrt{\frac{295.84+\sqrt{87095.296}}{2}}\) = \(\sqrt{296.0}\) = \(\mathtt{\text{17.2}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{0.6}}·\mathtt{\text{17.2}}}{2}\) = \(\mathtt{\text{5.16}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{17.2}}}{2}\) = \(\mathtt{\text{8.6}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{17.2}}}{2}\) = \(\mathtt{\text{8.6}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{17.2}}+0.6-\mathtt{\text{17.2}}}{2}\) = \(\mathtt{\text{0.3}}\)Периметр P:
P = \(a+b+c\) = \(\mathtt{\text{17.2}}+0.6+\mathtt{\text{17.2}}\) = \(\mathtt{\text{35}}\)
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