Расчет прямоугольного треугольника с катетом b=30 и углом α°=40
Калькулятор прямоугольного треугольника — это инструмент, который помогает вычислять различные параметры прямоугольного треугольника, такие как длина сторон, площадь, периметр,углы и высоты.
Ответ:
\(a=\mathtt{\text{25.2}}\)
\(b=30\)
\(c=\mathtt{\text{39.2}}\)
\(40\)°
\(\mathtt{\text{50}}\)°
h=\(\mathtt{\text{19.3}}\)
mc=\(\mathtt{\text{19.6}}\)
Гипотенуза c:
c = \(\frac{b}{\cos{α°}}\) = \(\frac{30}{\cos{(40°})}\) = \(\mathtt{\text{39.2}}\)Угол β°:
β° = \(90°-α°\) = \(90°-40°\) = \(\mathtt{\text{50}}°\)Высота h:
h = \(b·\sin{α°}\) = \(30·\sin{(40°)}\) = \(\mathtt{\text{19.3}}\)Катет a:
a = \(\sqrt{c^2 - b^2}\) = \(\sqrt{\mathtt{\text{39.2}}^2 -30^2}\) = \(\sqrt{1536.64-900}\) = \(\sqrt{636.64}\) = \(\mathtt{\text{25.2}}\)или:
a = \(h·\frac{c}{b}\) =\(\mathtt{\text{19.3}}·\frac{\mathtt{\text{39.2}}}{30}\) = \(\mathtt{\text{25.2}}\)или:
a = \(c·\sin{α°}\) = \(\mathtt{\text{39.2}}·\sin{(40°)}\) = \(\mathtt{\text{25.2}}\)или:
a = \(c·\cos{β°}\) = \(\mathtt{\text{39.2}}·\cos{(50°)}\) = \(\mathtt{\text{25.2}}\)или:
a = \(\frac{h}{cos{α°}}\) = \(\frac{\mathtt{\text{19.3}}}{cos{(40°)}}\) = \(\mathtt{\text{25.2}}\)или:
a = \(\frac{h}{sin{β°}}\) = \(\frac{(\mathtt{\text{19.3}})}{sin{(\mathtt{\text{50}}°)}}\) = \(\mathtt{\text{25.2}}\)или:
a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{39.2}}^2 + \sqrt{\mathtt{\text{39.2}}^4-4·\mathtt{\text{39.2}}^2·19.3^2}}{2}}\) = \(\sqrt{\frac{1536.64+\sqrt{71730.3552000006}}{2}}\) = \(\sqrt{902.0}\) = \(\mathtt{\text{30}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{19.3}}·\mathtt{\text{39.2}}}{2}\) = \(\mathtt{\text{378}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{39.2}}}{2}\) = \(\mathtt{\text{19.6}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{39.2}}}{2}\) = \(\mathtt{\text{19.6}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{25.2}}+30-\mathtt{\text{39.2}}}{2}\) = \(\mathtt{\text{8}}\)Периметр P:
P = \(a+b+c\) = \(\mathtt{\text{25.2}}+30+\mathtt{\text{39.2}}\) = \(\mathtt{\text{94.4}}\)
Сохраните ссылку на это решение:
Скопировано