Расчет прямоугольного треугольника с катетом a=3,8 и углом β°=10
Калькулятор прямоугольного треугольника — это инструмент, который помогает вычислять различные параметры прямоугольного треугольника, такие как длина сторон, площадь, периметр,углы и высоты.
Ответ:
\(a=3,8\)
\(b=\mathtt{\text{0.53}}\)
\(c=\mathtt{\text{3.05}}\)
\(\mathtt{\text{80}}\)°
\(10\)°
h=\(\mathtt{\text{0.521}}\)
mc=\(\mathtt{\text{1.52}}\)
Гипотенуза c:
c = \(\frac{a}{\cos{β°}}\) = \(\frac{3,8}{\cos{(10°})}\) = \(\mathtt{\text{3.05}}\)Угол α°:
α° = \(90°-β°\) = \(90°-10°\) = \(\mathtt{\text{80}}°\)Высота h:
h = \(a·\sin{β°}\) = \(3,8·\sin{(10°)}\) = \(\mathtt{\text{0.521}}\)Катет b:
b = \(\sqrt{c^2 - a^2}\) = \(\sqrt{\mathtt{\text{3.05}}^2-3,8^2}\) = \(\sqrt{9.3025-9}\) = \(\sqrt{0.302499999999998}\) = \(\mathtt{\text{0.55}}\)или:
b = \(h·\frac{c}{a}\) = \(\mathtt{\text{0.521}}·\frac{\mathtt{\text{3.05}}}{3,8}\) = \(\mathtt{\text{0.53}}\)или:
b = \(c·\cos{α°}\) = \(\mathtt{\text{3.05}}·\cos{(80°)}\) = \(\mathtt{\text{0.53}}\)или:
b = \(c·\sin{β°}\) = \(\mathtt{\text{3.05}}·\sin{(10°)}\) = \(\mathtt{\text{0.53}}\)или:
b = \(\frac{h}{sin{α°}}\) = \(\frac{\mathtt{\text{0.521}}}{sin{(80°)}}\) = \(\mathtt{\text{0.529}}\)или:
b = \(\frac{h}{sin{β°}}\) = \(\frac{\mathtt{\text{0.521}}}{sin{(10°)}}\) = \(\mathtt{\text{0.529}}\)или:
b = \(\sqrt{\frac{c^2 - \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{3.05}}^2 - \sqrt{\mathtt{\text{3.05}}^4-4·\mathtt{\text{3.05}}^2·\mathtt{\text{0.521}}^2}}{2}}\) = \(\sqrt{\frac{9.3025-\sqrt{76.43618664}}{2}}\) = \(\sqrt{0.28}\) = \(\mathtt{\text{0.529}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{0.521}}·\mathtt{\text{3.05}}}{2}\) = \(\mathtt{\text{0.795}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{3.05}}}{2}\) = \(\mathtt{\text{1.52}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{3.05}}}{2}\) = \(\mathtt{\text{1.52}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{3,8+\mathtt{\text{0.53}}-\mathtt{\text{3.05}}}{2}\) = \(\mathtt{\text{0.24}}\)Периметр P:
P = \(a+b+c\) = \(3,8+\mathtt{\text{0.53}}+\mathtt{\text{3.05}}\) = \(\mathtt{\text{6.58}}\)
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