Расчет прямоугольного треугольника с катетом b=0.6 и углом β°=50
Калькулятор прямоугольного треугольника — это инструмент, который помогает вычислять различные параметры прямоугольного треугольника, такие как длина сторон, площадь, периметр,углы и высоты.
Ответ:
\(a=\mathtt{\text{0.503}}\)
\(b=0.6\)
\(c=\mathtt{\text{0.783}}\)
\(\mathtt{\text{40}}\)°
\(50\)°
h=\(\mathtt{\text{0.386}}\)
mc=\(\mathtt{\text{0.392}}\)
Гипотенуза c:
c = \(\frac{b}{\sin{β°}}\) = \(\frac{0.6}{\sin{(50°})}\) = \(\mathtt{\text{0.783}}\)Угол α°:
α° = \(90°-β°\) = \(90°-50°\) = \(\mathtt{\text{40}}°\)Высота h:
h = \(b·\cos{β°}\) = \(0.6·\cos{(50°)}\) = \(\mathtt{\text{0.386}}\)Катет a:
a = \(\sqrt{c^2 - b^2}\) = \(\sqrt{\mathtt{\text{0.783}}^2 -0.6^2}\) = \(\sqrt{0.613089-0.36}\) = \(\sqrt{0.253089}\) = \(\mathtt{\text{0.503}}\)или:
a = \(h·\frac{c}{b}\) =\(\mathtt{\text{0.386}}·\frac{\mathtt{\text{0.783}}}{0.6}\) = \(\mathtt{\text{0.504}}\)или:
a = \(c·\sin{α°}\) = \(\mathtt{\text{0.783}}·\sin{(40°)}\) = \(\mathtt{\text{0.503}}\)или:
a = \(c·\cos{β°}\) = \(\mathtt{\text{0.783}}·\cos{(50°)}\) = \(\mathtt{\text{0.503}}\)или:
a = \(\frac{h}{cos{α°}}\) = \(\frac{\mathtt{\text{0.386}}}{cos{(40°)}}\) = \(\mathtt{\text{0.504}}\)или:
a = \(\frac{h}{sin{β°}}\) = \(\frac{(\mathtt{\text{0.386}})}{sin{(50°)}}\) = \(\mathtt{\text{0.504}}\)или:
a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{0.783}}^2 + \sqrt{\mathtt{\text{0.783}}^4-4·\mathtt{\text{0.783}}^2·0.386^2}}{2}}\) = \(\sqrt{\frac{0.613089+\sqrt{0.010486887345}}{2}}\) = \(\sqrt{0.358}\) = \(\mathtt{\text{0.598}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{0.386}}·\mathtt{\text{0.783}}}{2}\) = \(\mathtt{\text{0.151}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{0.783}}}{2}\) = \(\mathtt{\text{0.392}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{0.783}}}{2}\) = \(\mathtt{\text{0.392}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{0.503}}+0.6-\mathtt{\text{0.783}}}{2}\) = \(\mathtt{\text{0.16}}\)Периметр P:
P = \(a+b+c\) = \(\mathtt{\text{0.503}}+0.6+\mathtt{\text{0.783}}\) = \(\mathtt{\text{1.89}}\)
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