Расчет прямоугольного треугольника с катетом b=8 и углом α°=8
Калькулятор прямоугольного треугольника — это инструмент, который помогает вычислять различные параметры прямоугольного треугольника, такие как длина сторон, площадь, периметр,углы и высоты.
Ответ:
\(a=\mathtt{\text{1.13}}\)
\(b=8\)
\(c=\mathtt{\text{8.08}}\)
\(8\)°
\(\mathtt{\text{82}}\)°
h=\(\mathtt{\text{1.11}}\)
mc=\(\mathtt{\text{4.04}}\)
Гипотенуза c:
c = \(\frac{b}{\cos{α°}}\) = \(\frac{8}{\cos{(8°})}\) = \(\mathtt{\text{8.08}}\)Угол β°:
β° = \(90°-α°\) = \(90°-8°\) = \(\mathtt{\text{82}}°\)Высота h:
h = \(b·\sin{α°}\) = \(8·\sin{(8°)}\) = \(\mathtt{\text{1.11}}\)Катет a:
a = \(\sqrt{c^2 - b^2}\) = \(\sqrt{\mathtt{\text{8.08}}^2 -8^2}\) = \(\sqrt{65.2864-64}\) = \(\sqrt{1.2864}\) = \(\mathtt{\text{1.13}}\)или:
a = \(h·\frac{c}{b}\) =\(\mathtt{\text{1.11}}·\frac{\mathtt{\text{8.08}}}{8}\) = \(\mathtt{\text{1.12}}\)или:
a = \(c·\sin{α°}\) = \(\mathtt{\text{8.08}}·\sin{(8°)}\) = \(\mathtt{\text{1.12}}\)или:
a = \(c·\cos{β°}\) = \(\mathtt{\text{8.08}}·\cos{(82°)}\) = \(\mathtt{\text{1.12}}\)или:
a = \(\frac{h}{cos{α°}}\) = \(\frac{\mathtt{\text{1.11}}}{cos{(8°)}}\) = \(\mathtt{\text{1.12}}\)или:
a = \(\frac{h}{sin{β°}}\) = \(\frac{(\mathtt{\text{1.11}})}{sin{(\mathtt{\text{82}}°)}}\) = \(\mathtt{\text{1.12}}\)или:
a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{8.08}}^2 + \sqrt{\mathtt{\text{8.08}}^4-4·\mathtt{\text{8.08}}^2·1.11^2}}{2}}\) = \(\sqrt{\frac{65.2864+\sqrt{3940.5565312}}{2}}\) = \(\sqrt{64.0}\) = \(\mathtt{\text{8}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{1.11}}·\mathtt{\text{8.08}}}{2}\) = \(\mathtt{\text{4.48}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{8.08}}}{2}\) = \(\mathtt{\text{4.04}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{8.08}}}{2}\) = \(\mathtt{\text{4.04}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{1.13}}+8-\mathtt{\text{8.08}}}{2}\) = \(\mathtt{\text{0.525}}\)Периметр P:
P = \(a+b+c\) = \(\mathtt{\text{1.13}}+8+\mathtt{\text{8.08}}\) = \(\mathtt{\text{17.2}}\)
Сохраните ссылку на это решение:
Скопировано