Расчет прямоугольного треугольника с катетом b=7.5 и углом α°=9
Калькулятор прямоугольного треугольника — это инструмент, который помогает вычислять различные параметры прямоугольного треугольника, такие как длина сторон, площадь, периметр,углы и высоты.
Ответ:
\(a=\mathtt{\text{1.17}}\)
\(b=7.5\)
\(c=\mathtt{\text{7.59}}\)
\(9\)°
\(\mathtt{\text{81}}\)°
h=\(\mathtt{\text{1.17}}\)
mc=\(\mathtt{\text{3.79}}\)
Гипотенуза c:
c = \(\frac{b}{\cos{α°}}\) = \(\frac{7.5}{\cos{(9°})}\) = \(\mathtt{\text{7.59}}\)Угол β°:
β° = \(90°-α°\) = \(90°-9°\) = \(\mathtt{\text{81}}°\)Высота h:
h = \(b·\sin{α°}\) = \(7.5·\sin{(9°)}\) = \(\mathtt{\text{1.17}}\)Катет a:
a = \(\sqrt{c^2 - b^2}\) = \(\sqrt{\mathtt{\text{7.59}}^2 -7.5^2}\) = \(\sqrt{57.6081-56.25}\) = \(\sqrt{1.3581}\) = \(\mathtt{\text{1.17}}\)или:
a = \(h·\frac{c}{b}\) =\(\mathtt{\text{1.17}}·\frac{\mathtt{\text{7.59}}}{7.5}\) = \(\mathtt{\text{1.18}}\)или:
a = \(c·\sin{α°}\) = \(\mathtt{\text{7.59}}·\sin{(9°)}\) = \(\mathtt{\text{1.19}}\)или:
a = \(c·\cos{β°}\) = \(\mathtt{\text{7.59}}·\cos{(81°)}\) = \(\mathtt{\text{1.19}}\)или:
a = \(\frac{h}{cos{α°}}\) = \(\frac{\mathtt{\text{1.17}}}{cos{(9°)}}\) = \(\mathtt{\text{1.18}}\)или:
a = \(\frac{h}{sin{β°}}\) = \(\frac{(\mathtt{\text{1.17}})}{sin{(\mathtt{\text{81}}°)}}\) = \(\mathtt{\text{1.18}}\)или:
a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{7.59}}^2 + \sqrt{\mathtt{\text{7.59}}^4-4·\mathtt{\text{7.59}}^2·1.17^2}}{2}}\) = \(\sqrt{\frac{57.6081+\sqrt{3003.25427325}}{2}}\) = \(\sqrt{56.2}\) = \(\mathtt{\text{7.5}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{1.17}}·\mathtt{\text{7.59}}}{2}\) = \(\mathtt{\text{4.44}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{7.59}}}{2}\) = \(\mathtt{\text{3.79}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{7.59}}}{2}\) = \(\mathtt{\text{3.79}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{1.17}}+7.5-\mathtt{\text{7.59}}}{2}\) = \(\mathtt{\text{0.54}}\)Периметр P:
P = \(a+b+c\) = \(\mathtt{\text{1.17}}+7.5+\mathtt{\text{7.59}}\) = \(\mathtt{\text{16.3}}\)
Сохраните ссылку на это решение:
Скопировано