Расчет прямоугольного треугольника с катетом b=6000 и углом α°=5
Калькулятор прямоугольного треугольника — это инструмент, который помогает вычислять различные параметры прямоугольного треугольника, такие как длина сторон, площадь, периметр,углы и высоты.
Ответ:
\(a=\mathtt{\text{490}}\)
\(b=6000\)
\(c=\mathtt{\text{6.02e+03}}\)
\(5\)°
\(\mathtt{\text{85}}\)°
h=\(\mathtt{\text{523}}\)
mc=\(\mathtt{\text{3.01e+03}}\)
Гипотенуза c:
c = \(\frac{b}{\cos{α°}}\) = \(\frac{6000}{\cos{(5°})}\) = \(\mathtt{\text{6.02e+03}}\)Угол β°:
β° = \(90°-α°\) = \(90°-5°\) = \(\mathtt{\text{85}}°\)Высота h:
h = \(b·\sin{α°}\) = \(6000·\sin{(5°)}\) = \(\mathtt{\text{523}}\)Катет a:
a = \(\sqrt{c^2 - b^2}\) = \(\sqrt{\mathtt{\text{6.02e+03}}^2 -6000^2}\) = \(\sqrt{36240400.0-36000000}\) = \(\sqrt{240400.0}\) = \(\mathtt{\text{490}}\)или:
a = \(h·\frac{c}{b}\) =\(\mathtt{\text{523}}·\frac{\mathtt{\text{6.02e+03}}}{6000}\) = \(\mathtt{\text{525}}\)или:
a = \(c·\sin{α°}\) = \(\mathtt{\text{6.02e+03}}·\sin{(5°)}\) = \(\mathtt{\text{525}}\)или:
a = \(c·\cos{β°}\) = \(\mathtt{\text{6.02e+03}}·\cos{(85°)}\) = \(\mathtt{\text{525}}\)или:
a = \(\frac{h}{cos{α°}}\) = \(\frac{\mathtt{\text{523}}}{cos{(5°)}}\) = \(\mathtt{\text{525}}\)или:
a = \(\frac{h}{sin{β°}}\) = \(\frac{(\mathtt{\text{523}})}{sin{(\mathtt{\text{85}}°)}}\) = \(\mathtt{\text{525}}\)или:
a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{6.02e+03}}^2 + \sqrt{\mathtt{\text{6.02e+03}}^4-4·\mathtt{\text{6.02e+03}}^2·523^2}}{2}}\) = \(\sqrt{\frac{36240400.0+\sqrt{1.2737153906736 \cdot 10^{15}}}{2}}\) = \(\sqrt{3.6 \cdot 10^{7}}\) = \(\mathtt{\text{6e+03}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{523}}·\mathtt{\text{6.02e+03}}}{2}\) = \(\mathtt{\text{1.57e+06}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{6.02e+03}}}{2}\) = \(\mathtt{\text{3.01e+03}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{6.02e+03}}}{2}\) = \(\mathtt{\text{3.01e+03}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{490}}+6000-\mathtt{\text{6.02e+03}}}{2}\) = \(\mathtt{\text{235}}\)Периметр P:
P = \(a+b+c\) = \(\mathtt{\text{490}}+6000+\mathtt{\text{6.02e+03}}\) = \(\mathtt{\text{1.25e+04}}\)
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