Расчет прямоугольного треугольника с катетом b=30 и углом α°=67

Калькулятор прямоугольного треугольника — это инструмент, который помогает вычислять различные параметры прямоугольного треугольника, такие как длина сторон, площадь, периметр,углы и высоты.

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c = \(\frac{b}{\cos{α°}}\) = \(\frac{30}{\cos{(67°})}\) = \(\mathtt{\text{76.8}}\)

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β° = \(90°-α°\) = \(90°-67°\) = \(\mathtt{\text{23}}°\)

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h = \(b·\sin{α°}\) = \(30·\sin{(67°)}\) = \(\mathtt{\text{27.6}}\)

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a = \(\sqrt{c^2 - b^2}\) = \(\sqrt{\mathtt{\text{76.8}}^2 -30^2}\) = \(\sqrt{5898.24-900}\) = \(\sqrt{4998.24}\) = \(\mathtt{\text{70.7}}\)a = \(h·\frac{c}{b}\) =\(\mathtt{\text{27.6}}·\frac{\mathtt{\text{76.8}}}{30}\) = \(\mathtt{\text{70.7}}\)a = \(c·\sin{α°}\) = \(\mathtt{\text{76.8}}·\sin{(67°)}\) = \(\mathtt{\text{70.7}}\)a = \(c·\cos{β°}\) = \(\mathtt{\text{76.8}}·\cos{(23°)}\) = \(\mathtt{\text{70.7}}\)a = \(\frac{h}{cos{α°}}\) = \(\frac{\mathtt{\text{27.6}}}{cos{(67°)}}\) = \(\mathtt{\text{70.6}}\)a = \(\frac{h}{sin{β°}}\) = \(\frac{(\mathtt{\text{27.6}})}{sin{(\mathtt{\text{23}}°)}}\) = \(\mathtt{\text{70.6}}\)a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{76.8}}^2 + \sqrt{\mathtt{\text{76.8}}^4-4·\mathtt{\text{76.8}}^2·27.6^2}}{2}}\) = \(\sqrt{\frac{5898.24+\sqrt{16817061.888}}{2}}\) = \(\sqrt{5.0 \cdot 10^{3}}\) = \(\mathtt{\text{70.7}}\)

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S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{27.6}}·\mathtt{\text{76.8}}}{2}\) = \(\mathtt{\text{1.06e+03}}\)

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R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{76.8}}}{2}\) = \(\mathtt{\text{38.4}}\)

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mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{76.8}}}{2}\) = \(\mathtt{\text{38.4}}\)

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r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{70.7}}+30-\mathtt{\text{76.8}}}{2}\) = \(\mathtt{\text{12}}\)

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P = \(a+b+c\) = \(\mathtt{\text{70.7}}+30+\mathtt{\text{76.8}}\) = \(\mathtt{\text{178}}\)