Расчет прямоугольного треугольника с катетом b=6 и углом α°=22
Калькулятор прямоугольного треугольника — это инструмент, который помогает вычислять различные параметры прямоугольного треугольника, такие как длина сторон, площадь, периметр,углы и высоты.
Ответ:
\(a=\mathtt{\text{2.42}}\)
\(b=6\)
\(c=\mathtt{\text{6.47}}\)
\(22\)°
\(\mathtt{\text{68}}\)°
h=\(\mathtt{\text{2.25}}\)
mc=\(\mathtt{\text{3.23}}\)
Гипотенуза c:
c = \(\frac{b}{\cos{α°}}\) = \(\frac{6}{\cos{(22°})}\) = \(\mathtt{\text{6.47}}\)Угол β°:
β° = \(90°-α°\) = \(90°-22°\) = \(\mathtt{\text{68}}°\)Высота h:
h = \(b·\sin{α°}\) = \(6·\sin{(22°)}\) = \(\mathtt{\text{2.25}}\)Катет a:
a = \(\sqrt{c^2 - b^2}\) = \(\sqrt{\mathtt{\text{6.47}}^2 -6^2}\) = \(\sqrt{41.8609-36}\) = \(\sqrt{5.86089999999999}\) = \(\mathtt{\text{2.42}}\)или:
a = \(h·\frac{c}{b}\) =\(\mathtt{\text{2.25}}·\frac{\mathtt{\text{6.47}}}{6}\) = \(\mathtt{\text{2.43}}\)или:
a = \(c·\sin{α°}\) = \(\mathtt{\text{6.47}}·\sin{(22°)}\) = \(\mathtt{\text{2.42}}\)или:
a = \(c·\cos{β°}\) = \(\mathtt{\text{6.47}}·\cos{(68°)}\) = \(\mathtt{\text{2.42}}\)или:
a = \(\frac{h}{cos{α°}}\) = \(\frac{\mathtt{\text{2.25}}}{cos{(22°)}}\) = \(\mathtt{\text{2.43}}\)или:
a = \(\frac{h}{sin{β°}}\) = \(\frac{(\mathtt{\text{2.25}})}{sin{(\mathtt{\text{68}}°)}}\) = \(\mathtt{\text{2.43}}\)или:
a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{6.47}}^2 + \sqrt{\mathtt{\text{6.47}}^4-4·\mathtt{\text{6.47}}^2·2.25^2}}{2}}\) = \(\sqrt{\frac{41.8609+\sqrt{904.65172381}}{2}}\) = \(\sqrt{36.0}\) = \(\mathtt{\text{6}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{2.25}}·\mathtt{\text{6.47}}}{2}\) = \(\mathtt{\text{7.28}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{6.47}}}{2}\) = \(\mathtt{\text{3.23}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{6.47}}}{2}\) = \(\mathtt{\text{3.23}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{2.42}}+6-\mathtt{\text{6.47}}}{2}\) = \(\mathtt{\text{0.975}}\)Периметр P:
P = \(a+b+c\) = \(\mathtt{\text{2.42}}+6+\mathtt{\text{6.47}}\) = \(\mathtt{\text{14.9}}\)
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