Расчет прямоугольного треугольника с катетом b=0.6 и углом β°=80
Калькулятор прямоугольного треугольника — это инструмент, который помогает вычислять различные параметры прямоугольного треугольника, такие как длина сторон, площадь, периметр,углы и высоты.
Ответ:
\(a=\mathtt{\text{0.104}}\)
\(b=0.6\)
\(c=\mathtt{\text{0.609}}\)
\(\mathtt{\text{10}}\)°
\(80\)°
h=\(\mathtt{\text{0.104}}\)
mc=\(\mathtt{\text{0.304}}\)
Гипотенуза c:
c = \(\frac{b}{\sin{β°}}\) = \(\frac{0.6}{\sin{(80°})}\) = \(\mathtt{\text{0.609}}\)Угол α°:
α° = \(90°-β°\) = \(90°-80°\) = \(\mathtt{\text{10}}°\)Высота h:
h = \(b·\cos{β°}\) = \(0.6·\cos{(80°)}\) = \(\mathtt{\text{0.104}}\)Катет a:
a = \(\sqrt{c^2 - b^2}\) = \(\sqrt{\mathtt{\text{0.609}}^2 -0.6^2}\) = \(\sqrt{0.370881-0.36}\) = \(\sqrt{0.010881}\) = \(\mathtt{\text{0.104}}\)или:
a = \(h·\frac{c}{b}\) =\(\mathtt{\text{0.104}}·\frac{\mathtt{\text{0.609}}}{0.6}\) = \(\mathtt{\text{0.106}}\)или:
a = \(c·\sin{α°}\) = \(\mathtt{\text{0.609}}·\sin{(10°)}\) = \(\mathtt{\text{0.106}}\)или:
a = \(c·\cos{β°}\) = \(\mathtt{\text{0.609}}·\cos{(80°)}\) = \(\mathtt{\text{0.106}}\)или:
a = \(\frac{h}{cos{α°}}\) = \(\frac{\mathtt{\text{0.104}}}{cos{(10°)}}\) = \(\mathtt{\text{0.106}}\)или:
a = \(\frac{h}{sin{β°}}\) = \(\frac{(\mathtt{\text{0.104}})}{sin{(80°)}}\) = \(\mathtt{\text{0.106}}\)или:
a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{0.609}}^2 + \sqrt{\mathtt{\text{0.609}}^4-4·\mathtt{\text{0.609}}^2·0.104^2}}{2}}\) = \(\sqrt{\frac{0.370881+\sqrt{0.121506920577}}{2}}\) = \(\sqrt{0.36}\) = \(\mathtt{\text{0.6}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{0.104}}·\mathtt{\text{0.609}}}{2}\) = \(\mathtt{\text{0.0317}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{0.609}}}{2}\) = \(\mathtt{\text{0.304}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{0.609}}}{2}\) = \(\mathtt{\text{0.304}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{0.104}}+0.6-\mathtt{\text{0.609}}}{2}\) = \(\mathtt{\text{0.0475}}\)Периметр P:
P = \(a+b+c\) = \(\mathtt{\text{0.104}}+0.6+\mathtt{\text{0.609}}\) = \(\mathtt{\text{1.31}}\)
Сохраните ссылку на это решение:
Скопировано