Расчет прямоугольного треугольника с катетом b=20 и углом α°=20
Калькулятор прямоугольного треугольника — это инструмент, который помогает вычислять различные параметры прямоугольного треугольника, такие как длина сторон, площадь, периметр,углы и высоты.
Ответ:
\(a=\mathtt{\text{7.33}}\)
\(b=20\)
\(c=\mathtt{\text{21.3}}\)
\(20\)°
\(\mathtt{\text{70}}\)°
h=\(\mathtt{\text{6.84}}\)
mc=\(\mathtt{\text{10.7}}\)
Гипотенуза c:
c = \(\frac{b}{\cos{α°}}\) = \(\frac{20}{\cos{(20°})}\) = \(\mathtt{\text{21.3}}\)Угол β°:
β° = \(90°-α°\) = \(90°-20°\) = \(\mathtt{\text{70}}°\)Высота h:
h = \(b·\sin{α°}\) = \(20·\sin{(20°)}\) = \(\mathtt{\text{6.84}}\)Катет a:
a = \(\sqrt{c^2 - b^2}\) = \(\sqrt{\mathtt{\text{21.3}}^2 -20^2}\) = \(\sqrt{453.69-400}\) = \(\sqrt{53.6900000000001}\) = \(\mathtt{\text{7.33}}\)или:
a = \(h·\frac{c}{b}\) =\(\mathtt{\text{6.84}}·\frac{\mathtt{\text{21.3}}}{20}\) = \(\mathtt{\text{7.28}}\)или:
a = \(c·\sin{α°}\) = \(\mathtt{\text{21.3}}·\sin{(20°)}\) = \(\mathtt{\text{7.29}}\)или:
a = \(c·\cos{β°}\) = \(\mathtt{\text{21.3}}·\cos{(70°)}\) = \(\mathtt{\text{7.29}}\)или:
a = \(\frac{h}{cos{α°}}\) = \(\frac{\mathtt{\text{6.84}}}{cos{(20°)}}\) = \(\mathtt{\text{7.28}}\)или:
a = \(\frac{h}{sin{β°}}\) = \(\frac{(\mathtt{\text{6.84}})}{sin{(\mathtt{\text{70}}°)}}\) = \(\mathtt{\text{7.28}}\)или:
a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{21.3}}^2 + \sqrt{\mathtt{\text{21.3}}^4-4·\mathtt{\text{21.3}}^2·6.84^2}}{2}}\) = \(\sqrt{\frac{453.69+\sqrt{120929.980644}}{2}}\) = \(\sqrt{401.0}\) = \(\mathtt{\text{20}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{6.84}}·\mathtt{\text{21.3}}}{2}\) = \(\mathtt{\text{72.8}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{21.3}}}{2}\) = \(\mathtt{\text{10.7}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{21.3}}}{2}\) = \(\mathtt{\text{10.7}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{7.33}}+20-\mathtt{\text{21.3}}}{2}\) = \(\mathtt{\text{3.01}}\)Периметр P:
P = \(a+b+c\) = \(\mathtt{\text{7.33}}+20+\mathtt{\text{21.3}}\) = \(\mathtt{\text{48.6}}\)
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