Расчет прямоугольного треугольника с катетом b=821 и углом α°=3
Калькулятор прямоугольного треугольника — это инструмент, который помогает вычислять различные параметры прямоугольного треугольника, такие как длина сторон, площадь, периметр,углы и высоты.
Ответ:
\(a=\mathtt{\text{40.5}}\)
\(b=821\)
\(c=\mathtt{\text{822}}\)
\(3\)°
\(\mathtt{\text{87}}\)°
h=\(\mathtt{\text{43}}\)
mc=\(\mathtt{\text{411}}\)
Гипотенуза c:
c = \(\frac{b}{\cos{α°}}\) = \(\frac{821}{\cos{(3°})}\) = \(\mathtt{\text{822}}\)Угол β°:
β° = \(90°-α°\) = \(90°-3°\) = \(\mathtt{\text{87}}°\)Высота h:
h = \(b·\sin{α°}\) = \(821·\sin{(3°)}\) = \(\mathtt{\text{43}}\)Катет a:
a = \(\sqrt{c^2 - b^2}\) = \(\sqrt{\mathtt{\text{822}}^2 -821^2}\) = \(\sqrt{675684-674041}\) = \(\sqrt{1643}\) = \(\mathtt{\text{40.5}}\)или:
a = \(h·\frac{c}{b}\) =\(\mathtt{\text{43}}·\frac{\mathtt{\text{822}}}{821}\) = \(\mathtt{\text{43.1}}\)или:
a = \(c·\sin{α°}\) = \(\mathtt{\text{822}}·\sin{(3°)}\) = \(\mathtt{\text{43}}\)или:
a = \(c·\cos{β°}\) = \(\mathtt{\text{822}}·\cos{(87°)}\) = \(\mathtt{\text{43}}\)или:
a = \(\frac{h}{cos{α°}}\) = \(\frac{\mathtt{\text{43}}}{cos{(3°)}}\) = \(\mathtt{\text{43.1}}\)или:
a = \(\frac{h}{sin{β°}}\) = \(\frac{(\mathtt{\text{43}})}{sin{(\mathtt{\text{87}}°)}}\) = \(\mathtt{\text{43.1}}\)или:
a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{822}}^2 + \sqrt{\mathtt{\text{822}}^4-4·\mathtt{\text{822}}^2·43^2}}{2}}\) = \(\sqrt{\frac{675684+\sqrt{451551508992}}{2}}\) = \(\sqrt{6.74 \cdot 10^{5}}\) = \(\mathtt{\text{821}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{43}}·\mathtt{\text{822}}}{2}\) = \(\mathtt{\text{1.77e+04}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{822}}}{2}\) = \(\mathtt{\text{411}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{822}}}{2}\) = \(\mathtt{\text{411}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{40.5}}+821-\mathtt{\text{822}}}{2}\) = \(\mathtt{\text{19.8}}\)Периметр P:
P = \(a+b+c\) = \(\mathtt{\text{40.5}}+821+\mathtt{\text{822}}\) = \(\mathtt{\text{1.68e+03}}\)
Сохраните ссылку на это решение:
Скопировано