Расчет прямоугольного треугольника с катетом b=3,5 и углом α°=45
Калькулятор прямоугольного треугольника — это инструмент, который помогает вычислять различные параметры прямоугольного треугольника, такие как длина сторон, площадь, периметр,углы и высоты.
Ответ:
\(a=\mathtt{\text{3}}\)
\(b=3,5\)
\(c=\mathtt{\text{4.24}}\)
\(45\)°
\(\mathtt{\text{45}}\)°
h=\(\mathtt{\text{2.12}}\)
mc=\(\mathtt{\text{2.12}}\)
Гипотенуза c:
c = \(\frac{b}{\cos{α°}}\) = \(\frac{3,5}{\cos{(45°})}\) = \(\mathtt{\text{4.24}}\)Угол β°:
β° = \(90°-α°\) = \(90°-45°\) = \(\mathtt{\text{45}}°\)Высота h:
h = \(b·\sin{α°}\) = \(3,5·\sin{(45°)}\) = \(\mathtt{\text{2.12}}\)Катет a:
a = \(\sqrt{c^2 - b^2}\) = \(\sqrt{\mathtt{\text{4.24}}^2 -3,5^2}\) = \(\sqrt{17.9776-9}\) = \(\sqrt{8.9776}\) = \(\mathtt{\text{3}}\)или:
a = \(h·\frac{c}{b}\) =\(\mathtt{\text{2.12}}·\frac{\mathtt{\text{4.24}}}{3,5}\) = \(\mathtt{\text{3}}\)или:
a = \(c·\sin{α°}\) = \(\mathtt{\text{4.24}}·\sin{(45°)}\) = \(\mathtt{\text{3}}\)или:
a = \(c·\cos{β°}\) = \(\mathtt{\text{4.24}}·\cos{(45°)}\) = \(\mathtt{\text{3}}\)или:
a = \(\frac{h}{cos{α°}}\) = \(\frac{\mathtt{\text{2.12}}}{cos{(45°)}}\) = \(\mathtt{\text{3}}\)или:
a = \(\frac{h}{sin{β°}}\) = \(\frac{(\mathtt{\text{2.12}})}{sin{(\mathtt{\text{45}}°)}}\) = \(\mathtt{\text{3}}\)или:
a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{4.24}}^2 + \sqrt{\mathtt{\text{4.24}}^4-4·\mathtt{\text{4.24}}^2·2.12^2}}{2}}\) = \(\sqrt{\frac{17.9776+\sqrt{0}}{2}}\) = \(\sqrt{8.99}\) = \(\mathtt{\text{3}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{2.12}}·\mathtt{\text{4.24}}}{2}\) = \(\mathtt{\text{4.49}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{4.24}}}{2}\) = \(\mathtt{\text{2.12}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{4.24}}}{2}\) = \(\mathtt{\text{2.12}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{3}}+3,5-\mathtt{\text{4.24}}}{2}\) = \(\mathtt{\text{0.88}}\)Периметр P:
P = \(a+b+c\) = \(\mathtt{\text{3}}+3,5+\mathtt{\text{4.24}}\) = \(\mathtt{\text{10.2}}\)
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