Расчет прямоугольного треугольника с катетом b=3,5 и углом α°=40 и углом β°=50
Калькулятор прямоугольного треугольника — это инструмент, который помогает вычислять различные параметры прямоугольного треугольника, такие как длина сторон, площадь, периметр,углы и высоты.
Ответ:
\(a=\mathtt{\text{2.52}}\)
\(b=3,5\)
\(c=\mathtt{\text{3.92}}\)
\(40\)°
\(50\)°
h=\(\mathtt{\text{1.93}}\)
mc=\(\mathtt{\text{1.96}}\)
Гипотенуза c:
c = \(\frac{b}{\sin{β°}}\) = \(\frac{3,5}{\sin{(50°})}\) = \(\mathtt{\text{3.92}}\)или:
c = \(\frac{b}{\cos{α°}}\) = \(\frac{3,5}{\cos{(40°})}\) = \(\mathtt{\text{3.92}}\)Высота h:
h = \(b·\sin{α°}\) = \(3,5·\sin{(40°)}\) = \(\mathtt{\text{1.93}}\)или:
h = \(b·\cos{β°}\) = \(3,5·\cos{(50°)}\) = \(\mathtt{\text{1.93}}\)Катет a:
a = \(\sqrt{c^2 - b^2}\) = \(\sqrt{\mathtt{\text{3.92}}^2 -3,5^2}\) = \(\sqrt{15.3664-9}\) = \(\sqrt{6.3664}\) = \(\mathtt{\text{2.52}}\)или:
a = \(h·\frac{c}{b}\) =\(\mathtt{\text{1.93}}·\frac{\mathtt{\text{3.92}}}{3,5}\) = \(\mathtt{\text{2.52}}\)или:
a = \(c·\sin{α°}\) = \(\mathtt{\text{3.92}}·\sin{(40°)}\) = \(\mathtt{\text{2.52}}\)или:
a = \(c·\cos{β°}\) = \(\mathtt{\text{3.92}}·\cos{(50°)}\) = \(\mathtt{\text{2.52}}\)или:
a = \(\frac{h}{cos{α°}}\) = \(\frac{\mathtt{\text{1.93}}}{cos{(40°)}}\) = \(\mathtt{\text{2.52}}\)или:
a = \(\frac{h}{sin{β°}}\) = \(\frac{(\mathtt{\text{1.93}})}{sin{(50°)}}\) = \(\mathtt{\text{2.52}}\)или:
a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{3.92}}^2 + \sqrt{\mathtt{\text{3.92}}^4-4·\mathtt{\text{3.92}}^2·1.93^2}}{2}}\) = \(\sqrt{\frac{15.3664+\sqrt{7.17303551999998}}{2}}\) = \(\sqrt{9.02}\) = \(\mathtt{\text{3}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{1.93}}·\mathtt{\text{3.92}}}{2}\) = \(\mathtt{\text{3.78}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{3.92}}}{2}\) = \(\mathtt{\text{1.96}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{3.92}}}{2}\) = \(\mathtt{\text{1.96}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{2.52}}+3,5-\mathtt{\text{3.92}}}{2}\) = \(\mathtt{\text{0.8}}\)Периметр P:
P = \(a+b+c\) = \(\mathtt{\text{2.52}}+3,5+\mathtt{\text{3.92}}\) = \(\mathtt{\text{9.44}}\)
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