Расчет прямоугольного треугольника с катетом b=105 и углом β°=60
Калькулятор прямоугольного треугольника — это инструмент, который помогает вычислять различные параметры прямоугольного треугольника, такие как длина сторон, площадь, периметр,углы и высоты.
Ответ:
\(a=\mathtt{\text{60.1}}\)
\(b=105\)
\(c=\mathtt{\text{121}}\)
\(\mathtt{\text{30}}\)°
\(60\)°
h=\(\mathtt{\text{52.5}}\)
mc=\(\mathtt{\text{60.5}}\)
Гипотенуза c:
c = \(\frac{b}{\sin{β°}}\) = \(\frac{105}{\sin{(60°})}\) = \(\mathtt{\text{121}}\)Угол α°:
α° = \(90°-β°\) = \(90°-60°\) = \(\mathtt{\text{30}}°\)Высота h:
h = \(b·\cos{β°}\) = \(105·\cos{(60°)}\) = \(\mathtt{\text{52.5}}\)Катет a:
a = \(\sqrt{c^2 - b^2}\) = \(\sqrt{\mathtt{\text{121}}^2 -105^2}\) = \(\sqrt{14641-11025}\) = \(\sqrt{3616}\) = \(\mathtt{\text{60.1}}\)или:
a = \(h·\frac{c}{b}\) =\(\mathtt{\text{52.5}}·\frac{\mathtt{\text{121}}}{105}\) = \(\mathtt{\text{60.5}}\)или:
a = \(c·\sin{α°}\) = \(\mathtt{\text{121}}·\sin{(30°)}\) = \(\mathtt{\text{60.5}}\)или:
a = \(c·\cos{β°}\) = \(\mathtt{\text{121}}·\cos{(60°)}\) = \(\mathtt{\text{60.5}}\)или:
a = \(\frac{h}{cos{α°}}\) = \(\frac{\mathtt{\text{52.5}}}{cos{(30°)}}\) = \(\mathtt{\text{60.6}}\)или:
a = \(\frac{h}{sin{β°}}\) = \(\frac{(\mathtt{\text{52.5}})}{sin{(60°)}}\) = \(\mathtt{\text{60.6}}\)или:
a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{121}}^2 + \sqrt{\mathtt{\text{121}}^4-4·\mathtt{\text{121}}^2·52.5^2}}{2}}\) = \(\sqrt{\frac{14641+\sqrt{52941856.0}}{2}}\) = \(\sqrt{1.1 \cdot 10^{4}}\) = \(\mathtt{\text{105}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{52.5}}·\mathtt{\text{121}}}{2}\) = \(\mathtt{\text{3.18e+03}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{121}}}{2}\) = \(\mathtt{\text{60.5}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{121}}}{2}\) = \(\mathtt{\text{60.5}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{60.1}}+105-\mathtt{\text{121}}}{2}\) = \(\mathtt{\text{22}}\)Периметр P:
P = \(a+b+c\) = \(\mathtt{\text{60.1}}+105+\mathtt{\text{121}}\) = \(\mathtt{\text{286}}\)
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