Расчет прямоугольного треугольника с катетом b=8000 и углом α°=8
Калькулятор прямоугольного треугольника — это инструмент, который помогает вычислять различные параметры прямоугольного треугольника, такие как длина сторон, площадь, периметр,углы и высоты.
Ответ:
\(a=\mathtt{\text{1.13e+03}}\)
\(b=8000\)
\(c=\mathtt{\text{8.08e+03}}\)
\(8\)°
\(\mathtt{\text{82}}\)°
h=\(\mathtt{\text{1.11e+03}}\)
mc=\(\mathtt{\text{4.04e+03}}\)
Гипотенуза c:
c = \(\frac{b}{\cos{α°}}\) = \(\frac{8000}{\cos{(8°})}\) = \(\mathtt{\text{8.08e+03}}\)Угол β°:
β° = \(90°-α°\) = \(90°-8°\) = \(\mathtt{\text{82}}°\)Высота h:
h = \(b·\sin{α°}\) = \(8000·\sin{(8°)}\) = \(\mathtt{\text{1.11e+03}}\)Катет a:
a = \(\sqrt{c^2 - b^2}\) = \(\sqrt{\mathtt{\text{8.08e+03}}^2 -8000^2}\) = \(\sqrt{65286400.0-64000000}\) = \(\sqrt{1286400.0}\) = \(\mathtt{\text{1.13e+03}}\)или:
a = \(h·\frac{c}{b}\) =\(\mathtt{\text{1.11e+03}}·\frac{\mathtt{\text{8.08e+03}}}{8000}\) = \(\mathtt{\text{1.12e+03}}\)или:
a = \(c·\sin{α°}\) = \(\mathtt{\text{8.08e+03}}·\sin{(8°)}\) = \(\mathtt{\text{1.12e+03}}\)или:
a = \(c·\cos{β°}\) = \(\mathtt{\text{8.08e+03}}·\cos{(82°)}\) = \(\mathtt{\text{1.12e+03}}\)или:
a = \(\frac{h}{cos{α°}}\) = \(\frac{\mathtt{\text{1.11e+03}}}{cos{(8°)}}\) = \(\mathtt{\text{1.12e+03}}\)или:
a = \(\frac{h}{sin{β°}}\) = \(\frac{(\mathtt{\text{1.11e+03}})}{sin{(\mathtt{\text{82}}°)}}\) = \(\mathtt{\text{1.12e+03}}\)или:
a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{8.08e+03}}^2 + \sqrt{\mathtt{\text{8.08e+03}}^4-4·\mathtt{\text{8.08e+03}}^2·1.11e+03^2}}{2}}\) = \(\sqrt{\frac{65286400.0+\sqrt{3.9405565312 \cdot 10^{15}}}{2}}\) = \(\sqrt{6.4 \cdot 10^{7}}\) = \(\mathtt{\text{8e+03}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{1.11e+03}}·\mathtt{\text{8.08e+03}}}{2}\) = \(\mathtt{\text{4.48e+06}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{8.08e+03}}}{2}\) = \(\mathtt{\text{4.04e+03}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{8.08e+03}}}{2}\) = \(\mathtt{\text{4.04e+03}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{1.13e+03}}+8000-\mathtt{\text{8.08e+03}}}{2}\) = \(\mathtt{\text{525}}\)Периметр P:
P = \(a+b+c\) = \(\mathtt{\text{1.13e+03}}+8000+\mathtt{\text{8.08e+03}}\) = \(\mathtt{\text{1.72e+04}}\)
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