Расчет прямоугольного треугольника с катетом b=31 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:
\(a=\mathtt{\text{8.33}}\)
\(b=31\)
\(c=\mathtt{\text{32.1}}\)
\(15\)°
\(\mathtt{\text{75}}\)°
h=\(\mathtt{\text{8.02}}\)
mc=\(\mathtt{\text{16.1}}\)
Гипотенуза c:
c = \(\frac{b}{\cos{α°}}\) = \(\frac{31}{\cos{(15°})}\) = \(\mathtt{\text{32.1}}\)Угол β°:
β° = \(90°-α°\) = \(90°-15°\) = \(\mathtt{\text{75}}°\)Высота h:
h = \(b·\sin{α°}\) = \(31·\sin{(15°)}\) = \(\mathtt{\text{8.02}}\)Катет a:
a = \(\sqrt{c^2 - b^2}\) = \(\sqrt{\mathtt{\text{32.1}}^2 -31^2}\) = \(\sqrt{1030.41-961}\) = \(\sqrt{69.4100000000001}\) = \(\mathtt{\text{8.33}}\)или:
a = \(h·\frac{c}{b}\) =\(\mathtt{\text{8.02}}·\frac{\mathtt{\text{32.1}}}{31}\) = \(\mathtt{\text{8.3}}\)или:
a = \(c·\sin{α°}\) = \(\mathtt{\text{32.1}}·\sin{(15°)}\) = \(\mathtt{\text{8.31}}\)или:
a = \(c·\cos{β°}\) = \(\mathtt{\text{32.1}}·\cos{(75°)}\) = \(\mathtt{\text{8.31}}\)или:
a = \(\frac{h}{cos{α°}}\) = \(\frac{\mathtt{\text{8.02}}}{cos{(15°)}}\) = \(\mathtt{\text{8.3}}\)или:
a = \(\frac{h}{sin{β°}}\) = \(\frac{(\mathtt{\text{8.02}})}{sin{(\mathtt{\text{75}}°)}}\) = \(\mathtt{\text{8.3}}\)или:
a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{32.1}}^2 + \sqrt{\mathtt{\text{32.1}}^4-4·\mathtt{\text{32.1}}^2·8.02^2}}{2}}\) = \(\sqrt{\frac{1030.41+\sqrt{796639.234644}}{2}}\) = \(\sqrt{962.0}\) = \(\mathtt{\text{31}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{8.02}}·\mathtt{\text{32.1}}}{2}\) = \(\mathtt{\text{129}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{32.1}}}{2}\) = \(\mathtt{\text{16.1}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{32.1}}}{2}\) = \(\mathtt{\text{16.1}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{8.33}}+31-\mathtt{\text{32.1}}}{2}\) = \(\mathtt{\text{3.61}}\)Периметр P:
P = \(a+b+c\) = \(\mathtt{\text{8.33}}+31+\mathtt{\text{32.1}}\) = \(\mathtt{\text{71.4}}\)
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