Расчет прямоугольного треугольника с катетом b=0.6 и углом β°=87
Калькулятор прямоугольного треугольника — это инструмент, который помогает вычислять различные параметры прямоугольного треугольника, такие как длина сторон, площадь, периметр,углы и высоты.
Ответ:
\(a=\mathtt{\text{0.0347}}\)
\(b=0.6\)
\(c=\mathtt{\text{0.601}}\)
\(\mathtt{\text{3}}\)°
\(87\)°
h=\(\mathtt{\text{0.0314}}\)
mc=\(\mathtt{\text{0.3}}\)
Гипотенуза c:
c = \(\frac{b}{\sin{β°}}\) = \(\frac{0.6}{\sin{(87°})}\) = \(\mathtt{\text{0.601}}\)Угол α°:
α° = \(90°-β°\) = \(90°-87°\) = \(\mathtt{\text{3}}°\)Высота h:
h = \(b·\cos{β°}\) = \(0.6·\cos{(87°)}\) = \(\mathtt{\text{0.0314}}\)Катет a:
a = \(\sqrt{c^2 - b^2}\) = \(\sqrt{\mathtt{\text{0.601}}^2 -0.6^2}\) = \(\sqrt{0.361201-0.36}\) = \(\sqrt{0.00120100000000001}\) = \(\mathtt{\text{0.0347}}\)или:
a = \(h·\frac{c}{b}\) =\(\mathtt{\text{0.0314}}·\frac{\mathtt{\text{0.601}}}{0.6}\) = \(\mathtt{\text{0.0315}}\)или:
a = \(c·\sin{α°}\) = \(\mathtt{\text{0.601}}·\sin{(3°)}\) = \(\mathtt{\text{0.0315}}\)или:
a = \(c·\cos{β°}\) = \(\mathtt{\text{0.601}}·\cos{(87°)}\) = \(\mathtt{\text{0.0315}}\)или:
a = \(\frac{h}{cos{α°}}\) = \(\frac{\mathtt{\text{0.0314}}}{cos{(3°)}}\) = \(\mathtt{\text{0.0314}}\)или:
a = \(\frac{h}{sin{β°}}\) = \(\frac{(\mathtt{\text{0.0314}})}{sin{(87°)}}\) = \(\mathtt{\text{0.0314}}\)или:
a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{0.601}}^2 + \sqrt{\mathtt{\text{0.601}}^4-4·\mathtt{\text{0.601}}^2·0.0314^2}}{2}}\) = \(\sqrt{\frac{0.361201+\sqrt{0.12904164344916}}{2}}\) = \(\sqrt{0.36}\) = \(\mathtt{\text{0.6}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{0.0314}}·\mathtt{\text{0.601}}}{2}\) = \(\mathtt{\text{0.00944}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{0.601}}}{2}\) = \(\mathtt{\text{0.3}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{0.601}}}{2}\) = \(\mathtt{\text{0.3}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{0.0347}}+0.6-\mathtt{\text{0.601}}}{2}\) = \(\mathtt{\text{0.0168}}\)Периметр P:
P = \(a+b+c\) = \(\mathtt{\text{0.0347}}+0.6+\mathtt{\text{0.601}}\) = \(\mathtt{\text{1.24}}\)
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