Расчет прямоугольного треугольника с катетом b=7634 и углом α°=20
Калькулятор прямоугольного треугольника — это инструмент, который помогает вычислять различные параметры прямоугольного треугольника, такие как длина сторон, площадь, периметр,углы и высоты.
Ответ:
\(a=\mathtt{\text{2.77e+03}}\)
\(b=7634\)
\(c=\mathtt{\text{8.12e+03}}\)
\(20\)°
\(\mathtt{\text{70}}\)°
h=\(\mathtt{\text{2.61e+03}}\)
mc=\(\mathtt{\text{4.06e+03}}\)
Гипотенуза c:
c = \(\frac{b}{\cos{α°}}\) = \(\frac{7634}{\cos{(20°})}\) = \(\mathtt{\text{8.12e+03}}\)Угол β°:
β° = \(90°-α°\) = \(90°-20°\) = \(\mathtt{\text{70}}°\)Высота h:
h = \(b·\sin{α°}\) = \(7634·\sin{(20°)}\) = \(\mathtt{\text{2.61e+03}}\)Катет a:
a = \(\sqrt{c^2 - b^2}\) = \(\sqrt{\mathtt{\text{8.12e+03}}^2 -7634^2}\) = \(\sqrt{65934400.0-58277956}\) = \(\sqrt{7656444.0}\) = \(\mathtt{\text{2.77e+03}}\)или:
a = \(h·\frac{c}{b}\) =\(\mathtt{\text{2.61e+03}}·\frac{\mathtt{\text{8.12e+03}}}{7634}\) = \(\mathtt{\text{2.78e+03}}\)или:
a = \(c·\sin{α°}\) = \(\mathtt{\text{8.12e+03}}·\sin{(20°)}\) = \(\mathtt{\text{2.78e+03}}\)или:
a = \(c·\cos{β°}\) = \(\mathtt{\text{8.12e+03}}·\cos{(70°)}\) = \(\mathtt{\text{2.78e+03}}\)или:
a = \(\frac{h}{cos{α°}}\) = \(\frac{\mathtt{\text{2.61e+03}}}{cos{(20°)}}\) = \(\mathtt{\text{2.78e+03}}\)или:
a = \(\frac{h}{sin{β°}}\) = \(\frac{(\mathtt{\text{2.61e+03}})}{sin{(\mathtt{\text{70}}°)}}\) = \(\mathtt{\text{2.78e+03}}\)или:
a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{8.12e+03}}^2 + \sqrt{\mathtt{\text{8.12e+03}}^4-4·\mathtt{\text{8.12e+03}}^2·2.61e+03^2}}{2}}\) = \(\sqrt{\frac{65934400.0+\sqrt{2.5507381984 \cdot 10^{15}}}{2}}\) = \(\sqrt{5.82 \cdot 10^{7}}\) = \(\mathtt{\text{7.63e+03}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{2.61e+03}}·\mathtt{\text{8.12e+03}}}{2}\) = \(\mathtt{\text{1.06e+07}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{8.12e+03}}}{2}\) = \(\mathtt{\text{4.06e+03}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{8.12e+03}}}{2}\) = \(\mathtt{\text{4.06e+03}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{2.77e+03}}+7634-\mathtt{\text{8.12e+03}}}{2}\) = \(\mathtt{\text{1.14e+03}}\)Периметр P:
P = \(a+b+c\) = \(\mathtt{\text{2.77e+03}}+7634+\mathtt{\text{8.12e+03}}\) = \(\mathtt{\text{1.85e+04}}\)
Сохраните ссылку на это решение:
Скопировано