Расчет прямоугольного треугольника с катетом b=76,34 и углом α°=20
Калькулятор прямоугольного треугольника — это инструмент, который помогает вычислять различные параметры прямоугольного треугольника, такие как длина сторон, площадь, периметр,углы и высоты.
Ответ:
\(a=\mathtt{\text{27.7}}\)
\(b=76,34\)
\(c=\mathtt{\text{80.9}}\)
\(20\)°
\(\mathtt{\text{70}}\)°
h=\(\mathtt{\text{26}}\)
mc=\(\mathtt{\text{40.5}}\)
Гипотенуза c:
c = \(\frac{b}{\cos{α°}}\) = \(\frac{76,34}{\cos{(20°})}\) = \(\mathtt{\text{80.9}}\)Угол β°:
β° = \(90°-α°\) = \(90°-20°\) = \(\mathtt{\text{70}}°\)Высота h:
h = \(b·\sin{α°}\) = \(76,34·\sin{(20°)}\) = \(\mathtt{\text{26}}\)Катет a:
a = \(\sqrt{c^2 - b^2}\) = \(\sqrt{\mathtt{\text{80.9}}^2 -76,34^2}\) = \(\sqrt{6544.81-5776}\) = \(\sqrt{768.810000000001}\) = \(\mathtt{\text{27.7}}\)или:
a = \(h·\frac{c}{b}\) =\(\mathtt{\text{26}}·\frac{\mathtt{\text{80.9}}}{76,34}\) = \(\mathtt{\text{27.7}}\)или:
a = \(c·\sin{α°}\) = \(\mathtt{\text{80.9}}·\sin{(20°)}\) = \(\mathtt{\text{27.7}}\)или:
a = \(c·\cos{β°}\) = \(\mathtt{\text{80.9}}·\cos{(70°)}\) = \(\mathtt{\text{27.7}}\)или:
a = \(\frac{h}{cos{α°}}\) = \(\frac{\mathtt{\text{26}}}{cos{(20°)}}\) = \(\mathtt{\text{27.7}}\)или:
a = \(\frac{h}{sin{β°}}\) = \(\frac{(\mathtt{\text{26}})}{sin{(\mathtt{\text{70}}°)}}\) = \(\mathtt{\text{27.7}}\)или:
a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{80.9}}^2 + \sqrt{\mathtt{\text{80.9}}^4-4·\mathtt{\text{80.9}}^2·26^2}}{2}}\) = \(\sqrt{\frac{6544.81+\sqrt{25137371.6961}}{2}}\) = \(\sqrt{5.78 \cdot 10^{3}}\) = \(\mathtt{\text{76}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{26}}·\mathtt{\text{80.9}}}{2}\) = \(\mathtt{\text{1.05e+03}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{80.9}}}{2}\) = \(\mathtt{\text{40.5}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{80.9}}}{2}\) = \(\mathtt{\text{40.5}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{27.7}}+76,34-\mathtt{\text{80.9}}}{2}\) = \(\mathtt{\text{11.4}}\)Периметр P:
P = \(a+b+c\) = \(\mathtt{\text{27.7}}+76,34+\mathtt{\text{80.9}}\) = \(\mathtt{\text{185}}\)
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