Расчет прямоугольного треугольника с катетом b=921 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:
\(a=\mathtt{\text{42.9}}\)
\(b=921\)
\(c=\mathtt{\text{922}}\)
\(3\)°
\(\mathtt{\text{87}}\)°
h=\(\mathtt{\text{48.2}}\)
mc=\(\mathtt{\text{461}}\)
Гипотенуза c:
c = \(\frac{b}{\cos{α°}}\) = \(\frac{921}{\cos{(3°})}\) = \(\mathtt{\text{922}}\)Угол β°:
β° = \(90°-α°\) = \(90°-3°\) = \(\mathtt{\text{87}}°\)Высота h:
h = \(b·\sin{α°}\) = \(921·\sin{(3°)}\) = \(\mathtt{\text{48.2}}\)Катет a:
a = \(\sqrt{c^2 - b^2}\) = \(\sqrt{\mathtt{\text{922}}^2 -921^2}\) = \(\sqrt{850084-848241}\) = \(\sqrt{1843}\) = \(\mathtt{\text{42.9}}\)или:
a = \(h·\frac{c}{b}\) =\(\mathtt{\text{48.2}}·\frac{\mathtt{\text{922}}}{921}\) = \(\mathtt{\text{48.3}}\)или:
a = \(c·\sin{α°}\) = \(\mathtt{\text{922}}·\sin{(3°)}\) = \(\mathtt{\text{48.3}}\)или:
a = \(c·\cos{β°}\) = \(\mathtt{\text{922}}·\cos{(87°)}\) = \(\mathtt{\text{48.3}}\)или:
a = \(\frac{h}{cos{α°}}\) = \(\frac{\mathtt{\text{48.2}}}{cos{(3°)}}\) = \(\mathtt{\text{48.3}}\)или:
a = \(\frac{h}{sin{β°}}\) = \(\frac{(\mathtt{\text{48.2}})}{sin{(\mathtt{\text{87}}°)}}\) = \(\mathtt{\text{48.3}}\)или:
a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{922}}^2 + \sqrt{\mathtt{\text{922}}^4-4·\mathtt{\text{922}}^2·48.2^2}}{2}}\) = \(\sqrt{\frac{850084+\sqrt{714743010447.36}}{2}}\) = \(\sqrt{8.48 \cdot 10^{5}}\) = \(\mathtt{\text{921}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{48.2}}·\mathtt{\text{922}}}{2}\) = \(\mathtt{\text{2.22e+04}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{922}}}{2}\) = \(\mathtt{\text{461}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{922}}}{2}\) = \(\mathtt{\text{461}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{42.9}}+921-\mathtt{\text{922}}}{2}\) = \(\mathtt{\text{20.9}}\)Периметр P:
P = \(a+b+c\) = \(\mathtt{\text{42.9}}+921+\mathtt{\text{922}}\) = \(\mathtt{\text{1.89e+03}}\)
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