Расчет прямоугольного треугольника с высотой h=16 и радиусом описанной окружности R=19

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 = \(2·R\) = \(2·19\) = \(\mathtt{\text{38}}\)

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a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{38}}^2 + \sqrt{\mathtt{\text{38}}^4-4·\mathtt{\text{38}}^2·16^2}}{2}}\) = \(\sqrt{\frac{1444+\sqrt{606480}}{2}}\) = \(\sqrt{1.11 \cdot 10^{3}}\) = \(\mathtt{\text{33.3}}\)

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b = \(\sqrt{\frac{c^2 - \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{38}}^2 - \sqrt{\mathtt{\text{38}}^4-4·\mathtt{\text{38}}^2·16^2}}{2}}\) = \(\sqrt{\frac{1444-\sqrt{606480}}{2}}\) = \(\sqrt{333.0}\) = \(\mathtt{\text{18.2}}\)

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S = \(\frac{hc}{2}\) = \(\frac{16·\mathtt{\text{38}}}{2}\) = \(\mathtt{\text{304}}\)

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mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{38}}}{2}\) = \(\mathtt{\text{19}}\)

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α° = \(\arcsin{\frac{a}{c}}\) = \(\arcsin{\frac{\mathtt{\text{33.3}}}{\mathtt{\text{38}}}}\) = \(\arcsin({0.88})\) = \(\mathtt{\text{61.2}}°\)

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β° =\(\arccos{\frac{a}{c}}\) = \(\arccos{\frac{\mathtt{\text{33.3}}}{\mathtt{\text{38}}}}\) = \(\arccos({0.88})\) = \(\mathtt{\text{28.8}}°\)

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r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{33.3}}+\mathtt{\text{18.2}}-\mathtt{\text{38}}}{2}\) = \(\mathtt{\text{6.75}}\)

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P = \(a+b+c\) = \(\mathtt{\text{33.3}}+\mathtt{\text{18.2}}+\mathtt{\text{38}}\) = \(\mathtt{\text{89.5}}\)