Расчет прямоугольного треугольника с катетом a=3.08 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:
\(a=3.08\)
\(b=\mathtt{\text{3.09}}\)
\(c=\mathtt{\text{4.36}}\)
\(45\)°
\(\mathtt{\text{45}}\)°
h=\(\mathtt{\text{2.18}}\)
mc=\(\mathtt{\text{2.18}}\)
Гипотенуза c:
c = \(\frac{a}{\sin{α°}}\) = \(\frac{3.08}{\sin{(45°})}\) = \(\mathtt{\text{4.36}}\)Угол β°:
β° = \(90°-α°\) = \(90°-45°\) = \(\mathtt{\text{45}}°\)Высота h:
h = \(a·\cos{α°}\) = \(3.08·\cos{(45°)}\) = \(\mathtt{\text{2.18}}\)Катет b:
b = \(\sqrt{c^2 - a^2}\) = \(\sqrt{\mathtt{\text{4.36}}^2-3.08^2}\) = \(\sqrt{19.0096-9.4864}\) = \(\sqrt{9.5232}\) = \(\mathtt{\text{3.09}}\)или:
b = \(h·\frac{c}{a}\) = \(\mathtt{\text{2.18}}·\frac{\mathtt{\text{4.36}}}{3.08}\) = \(\mathtt{\text{3.09}}\)или:
b = \(c·\cos{α°}\) = \(\mathtt{\text{4.36}}·\cos{(45°)}\) = \(\mathtt{\text{3.08}}\)или:
b = \(c·\sin{β°}\) = \(\mathtt{\text{4.36}}·\sin{(45°)}\) = \(\mathtt{\text{3.08}}\)или:
b = \(\frac{h}{sin{α°}}\) = \(\frac{\mathtt{\text{2.18}}}{sin{(45°)}}\) = \(\mathtt{\text{3.08}}\)или:
b = \(\frac{h}{sin{β°}}\) = \(\frac{\mathtt{\text{2.18}}}{sin{(45°)}}\) = \(\mathtt{\text{3.08}}\)или:
b = \(\sqrt{\frac{c^2 - \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{4.36}}^2 - \sqrt{\mathtt{\text{4.36}}^4-4·\mathtt{\text{4.36}}^2·\mathtt{\text{2.18}}^2}}{2}}\) = \(\sqrt{\frac{19.0096-\sqrt{5.6843418860808 \cdot 10^{-14}}}{2}}\) = \(\sqrt{9.5}\) = \(\mathtt{\text{3.08}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{2.18}}·\mathtt{\text{4.36}}}{2}\) = \(\mathtt{\text{4.75}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{4.36}}}{2}\) = \(\mathtt{\text{2.18}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{4.36}}}{2}\) = \(\mathtt{\text{2.18}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{3.08+\mathtt{\text{3.09}}-\mathtt{\text{4.36}}}{2}\) = \(\mathtt{\text{0.905}}\)Периметр P:
P = \(a+b+c\) = \(3.08+\mathtt{\text{3.09}}+\mathtt{\text{4.36}}\) = \(\mathtt{\text{10.5}}\)
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