Расчет прямоугольного треугольника с катетом b=2.4 и углом α°=20
Калькулятор прямоугольного треугольника — это инструмент, который помогает вычислять различные параметры прямоугольного треугольника, такие как длина сторон, площадь, периметр,углы и высоты.
Ответ:
\(a=\mathtt{\text{0.862}}\)
\(b=2.4\)
\(c=\mathtt{\text{2.55}}\)
\(20\)°
\(\mathtt{\text{70}}\)°
h=\(\mathtt{\text{0.821}}\)
mc=\(\mathtt{\text{1.27}}\)
Гипотенуза c:
c = \(\frac{b}{\cos{α°}}\) = \(\frac{2.4}{\cos{(20°})}\) = \(\mathtt{\text{2.55}}\)Угол β°:
β° = \(90°-α°\) = \(90°-20°\) = \(\mathtt{\text{70}}°\)Высота h:
h = \(b·\sin{α°}\) = \(2.4·\sin{(20°)}\) = \(\mathtt{\text{0.821}}\)Катет a:
a = \(\sqrt{c^2 - b^2}\) = \(\sqrt{\mathtt{\text{2.55}}^2 -2.4^2}\) = \(\sqrt{6.5025-5.76}\) = \(\sqrt{0.7425}\) = \(\mathtt{\text{0.862}}\)или:
a = \(h·\frac{c}{b}\) =\(\mathtt{\text{0.821}}·\frac{\mathtt{\text{2.55}}}{2.4}\) = \(\mathtt{\text{0.872}}\)или:
a = \(c·\sin{α°}\) = \(\mathtt{\text{2.55}}·\sin{(20°)}\) = \(\mathtt{\text{0.872}}\)или:
a = \(c·\cos{β°}\) = \(\mathtt{\text{2.55}}·\cos{(70°)}\) = \(\mathtt{\text{0.872}}\)или:
a = \(\frac{h}{cos{α°}}\) = \(\frac{\mathtt{\text{0.821}}}{cos{(20°)}}\) = \(\mathtt{\text{0.874}}\)или:
a = \(\frac{h}{sin{β°}}\) = \(\frac{(\mathtt{\text{0.821}})}{sin{(\mathtt{\text{70}}°)}}\) = \(\mathtt{\text{0.874}}\)или:
a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{2.55}}^2 + \sqrt{\mathtt{\text{2.55}}^4-4·\mathtt{\text{2.55}}^2·0.821^2}}{2}}\) = \(\sqrt{\frac{6.5025+\sqrt{24.75069984}}{2}}\) = \(\sqrt{5.74}\) = \(\mathtt{\text{2.4}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{0.821}}·\mathtt{\text{2.55}}}{2}\) = \(\mathtt{\text{1.05}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{2.55}}}{2}\) = \(\mathtt{\text{1.27}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{2.55}}}{2}\) = \(\mathtt{\text{1.27}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{0.862}}+2.4-\mathtt{\text{2.55}}}{2}\) = \(\mathtt{\text{0.356}}\)Периметр P:
P = \(a+b+c\) = \(\mathtt{\text{0.862}}+2.4+\mathtt{\text{2.55}}\) = \(\mathtt{\text{5.81}}\)
Сохраните ссылку на это решение:
Скопировано