Расчет прямоугольного треугольника с катетом b=465 и углом α°=10
Калькулятор прямоугольного треугольника — это инструмент, который помогает вычислять различные параметры прямоугольного треугольника, такие как длина сторон, площадь, периметр,углы и высоты.
Ответ:
\(a=\mathtt{\text{81}}\)
\(b=465\)
\(c=\mathtt{\text{472}}\)
\(10\)°
\(\mathtt{\text{80}}\)°
h=\(\mathtt{\text{80.7}}\)
mc=\(\mathtt{\text{236}}\)
Гипотенуза c:
c = \(\frac{b}{\cos{α°}}\) = \(\frac{465}{\cos{(10°})}\) = \(\mathtt{\text{472}}\)Угол β°:
β° = \(90°-α°\) = \(90°-10°\) = \(\mathtt{\text{80}}°\)Высота h:
h = \(b·\sin{α°}\) = \(465·\sin{(10°)}\) = \(\mathtt{\text{80.7}}\)Катет a:
a = \(\sqrt{c^2 - b^2}\) = \(\sqrt{\mathtt{\text{472}}^2 -465^2}\) = \(\sqrt{222784-216225}\) = \(\sqrt{6559}\) = \(\mathtt{\text{81}}\)или:
a = \(h·\frac{c}{b}\) =\(\mathtt{\text{80.7}}·\frac{\mathtt{\text{472}}}{465}\) = \(\mathtt{\text{81.9}}\)или:
a = \(c·\sin{α°}\) = \(\mathtt{\text{472}}·\sin{(10°)}\) = \(\mathtt{\text{82}}\)или:
a = \(c·\cos{β°}\) = \(\mathtt{\text{472}}·\cos{(80°)}\) = \(\mathtt{\text{82}}\)или:
a = \(\frac{h}{cos{α°}}\) = \(\frac{\mathtt{\text{80.7}}}{cos{(10°)}}\) = \(\mathtt{\text{81.9}}\)или:
a = \(\frac{h}{sin{β°}}\) = \(\frac{(\mathtt{\text{80.7}})}{sin{(\mathtt{\text{80}}°)}}\) = \(\mathtt{\text{81.9}}\)или:
a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{472}}^2 + \sqrt{\mathtt{\text{472}}^4-4·\mathtt{\text{472}}^2·80.7^2}}{2}}\) = \(\sqrt{\frac{222784+\sqrt{43829196367.36}}{2}}\) = \(\sqrt{2.16 \cdot 10^{5}}\) = \(\mathtt{\text{465}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{80.7}}·\mathtt{\text{472}}}{2}\) = \(\mathtt{\text{1.9e+04}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{472}}}{2}\) = \(\mathtt{\text{236}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{472}}}{2}\) = \(\mathtt{\text{236}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{81}}+465-\mathtt{\text{472}}}{2}\) = \(\mathtt{\text{37}}\)Периметр P:
P = \(a+b+c\) = \(\mathtt{\text{81}}+465+\mathtt{\text{472}}\) = \(\mathtt{\text{1.02e+03}}\)
Сохраните ссылку на это решение:
Скопировано