Расчет прямоугольного треугольника с катетом b=20,49 и углом α°=15
Калькулятор прямоугольного треугольника — это инструмент, который помогает вычислять различные параметры прямоугольного треугольника, такие как длина сторон, площадь, периметр,углы и высоты.
Ответ:
\(a=\mathtt{\text{5.34}}\)
\(b=20,49\)
\(c=\mathtt{\text{20.7}}\)
\(15\)°
\(\mathtt{\text{75}}\)°
h=\(\mathtt{\text{5.18}}\)
mc=\(\mathtt{\text{10.3}}\)
Гипотенуза c:
c = \(\frac{b}{\cos{α°}}\) = \(\frac{20,49}{\cos{(15°})}\) = \(\mathtt{\text{20.7}}\)Угол β°:
β° = \(90°-α°\) = \(90°-15°\) = \(\mathtt{\text{75}}°\)Высота h:
h = \(b·\sin{α°}\) = \(20,49·\sin{(15°)}\) = \(\mathtt{\text{5.18}}\)Катет a:
a = \(\sqrt{c^2 - b^2}\) = \(\sqrt{\mathtt{\text{20.7}}^2 -20,49^2}\) = \(\sqrt{428.49-400}\) = \(\sqrt{28.49}\) = \(\mathtt{\text{5.34}}\)или:
a = \(h·\frac{c}{b}\) =\(\mathtt{\text{5.18}}·\frac{\mathtt{\text{20.7}}}{20,49}\) = \(\mathtt{\text{5.36}}\)или:
a = \(c·\sin{α°}\) = \(\mathtt{\text{20.7}}·\sin{(15°)}\) = \(\mathtt{\text{5.36}}\)или:
a = \(c·\cos{β°}\) = \(\mathtt{\text{20.7}}·\cos{(75°)}\) = \(\mathtt{\text{5.36}}\)или:
a = \(\frac{h}{cos{α°}}\) = \(\frac{\mathtt{\text{5.18}}}{cos{(15°)}}\) = \(\mathtt{\text{5.36}}\)или:
a = \(\frac{h}{sin{β°}}\) = \(\frac{(\mathtt{\text{5.18}})}{sin{(\mathtt{\text{75}}°)}}\) = \(\mathtt{\text{5.36}}\)или:
a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{20.7}}^2 + \sqrt{\mathtt{\text{20.7}}^4-4·\mathtt{\text{20.7}}^2·5.18^2}}{2}}\) = \(\sqrt{\frac{428.49+\sqrt{137614.019796}}{2}}\) = \(\sqrt{400.0}\) = \(\mathtt{\text{20}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{5.18}}·\mathtt{\text{20.7}}}{2}\) = \(\mathtt{\text{53.6}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{20.7}}}{2}\) = \(\mathtt{\text{10.3}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{20.7}}}{2}\) = \(\mathtt{\text{10.3}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{5.34}}+20,49-\mathtt{\text{20.7}}}{2}\) = \(\mathtt{\text{2.32}}\)Периметр P:
P = \(a+b+c\) = \(\mathtt{\text{5.34}}+20,49+\mathtt{\text{20.7}}\) = \(\mathtt{\text{46}}\)
Сохраните ссылку на это решение:
Скопировано