Расчет прямоугольного треугольника с катетом b=3.6 и углом α°=30
Калькулятор прямоугольного треугольника — это инструмент, который помогает вычислять различные параметры прямоугольного треугольника, такие как длина сторон, площадь, периметр,углы и высоты.
Ответ:
\(a=\mathtt{\text{2.08}}\)
\(b=3.6\)
\(c=\mathtt{\text{4.16}}\)
\(30\)°
\(\mathtt{\text{60}}\)°
h=\(\mathtt{\text{1.8}}\)
mc=\(\mathtt{\text{2.08}}\)
Гипотенуза c:
c = \(\frac{b}{\cos{α°}}\) = \(\frac{3.6}{\cos{(30°})}\) = \(\mathtt{\text{4.16}}\)Угол β°:
β° = \(90°-α°\) = \(90°-30°\) = \(\mathtt{\text{60}}°\)Высота h:
h = \(b·\sin{α°}\) = \(3.6·\sin{(30°)}\) = \(\mathtt{\text{1.8}}\)Катет a:
a = \(\sqrt{c^2 - b^2}\) = \(\sqrt{\mathtt{\text{4.16}}^2 -3.6^2}\) = \(\sqrt{17.3056-12.96}\) = \(\sqrt{4.3456}\) = \(\mathtt{\text{2.08}}\)или:
a = \(h·\frac{c}{b}\) =\(\mathtt{\text{1.8}}·\frac{\mathtt{\text{4.16}}}{3.6}\) = \(\mathtt{\text{2.08}}\)или:
a = \(c·\sin{α°}\) = \(\mathtt{\text{4.16}}·\sin{(30°)}\) = \(\mathtt{\text{2.08}}\)или:
a = \(c·\cos{β°}\) = \(\mathtt{\text{4.16}}·\cos{(60°)}\) = \(\mathtt{\text{2.08}}\)или:
a = \(\frac{h}{cos{α°}}\) = \(\frac{\mathtt{\text{1.8}}}{cos{(30°)}}\) = \(\mathtt{\text{2.08}}\)или:
a = \(\frac{h}{sin{β°}}\) = \(\frac{(\mathtt{\text{1.8}})}{sin{(\mathtt{\text{60}}°)}}\) = \(\mathtt{\text{2.08}}\)или:
a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{4.16}}^2 + \sqrt{\mathtt{\text{4.16}}^4-4·\mathtt{\text{4.16}}^2·1.8^2}}{2}}\) = \(\sqrt{\frac{17.3056+\sqrt{75.20321536}}{2}}\) = \(\sqrt{13.0}\) = \(\mathtt{\text{3.6}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{1.8}}·\mathtt{\text{4.16}}}{2}\) = \(\mathtt{\text{3.74}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{4.16}}}{2}\) = \(\mathtt{\text{2.08}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{4.16}}}{2}\) = \(\mathtt{\text{2.08}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{2.08}}+3.6-\mathtt{\text{4.16}}}{2}\) = \(\mathtt{\text{0.76}}\)Периметр P:
P = \(a+b+c\) = \(\mathtt{\text{2.08}}+3.6+\mathtt{\text{4.16}}\) = \(\mathtt{\text{9.84}}\)
Сохраните ссылку на это решение:
Скопировано