Расчет прямоугольного треугольника с катетом a=10 и углом α°=40

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 = \(\frac{a}{\sin{α°}}\) = \(\frac{10}{\sin{(40°})}\) = \(\mathtt{\text{15.6}}\)

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β° = \(90°-α°\) = \(90°-40°\) = \(\mathtt{\text{50}}°\)

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h = \(a·\cos{α°}\) = \(10·\cos{(40°)}\) = \(\mathtt{\text{7.66}}\)

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b = \(\sqrt{c^2 - a^2}\) = \(\sqrt{\mathtt{\text{15.6}}^2-10^2}\) = \(\sqrt{243.36-100}\) = \(\sqrt{143.36}\) = \(\mathtt{\text{12}}\)b = \(h·\frac{c}{a}\) = \(\mathtt{\text{7.66}}·\frac{\mathtt{\text{15.6}}}{10}\) = \(\mathtt{\text{11.9}}\)b = \(c·\cos{α°}\) = \(\mathtt{\text{15.6}}·\cos{(40°)}\) = \(\mathtt{\text{12}}\)b = \(c·\sin{β°}\) = \(\mathtt{\text{15.6}}·\sin{(50°)}\) = \(\mathtt{\text{12}}\)b = \(\frac{h}{sin{α°}}\) = \(\frac{\mathtt{\text{7.66}}}{sin{(40°)}}\) = \(\mathtt{\text{11.9}}\)b = \(\frac{h}{sin{β°}}\) = \(\frac{\mathtt{\text{7.66}}}{sin{(50°)}}\) = \(\mathtt{\text{11.9}}\)b = \(\sqrt{\frac{c^2 - \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{15.6}}^2 - \sqrt{\mathtt{\text{15.6}}^4-4·\mathtt{\text{15.6}}^2·\mathtt{\text{7.66}}^2}}{2}}\) = \(\sqrt{\frac{243.36-\sqrt{2106.91353599999}}{2}}\) = \(\sqrt{98.7}\) = \(\mathtt{\text{9.94}}\)

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S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{7.66}}·\mathtt{\text{15.6}}}{2}\) = \(\mathtt{\text{59.7}}\)

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R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{15.6}}}{2}\) = \(\mathtt{\text{7.8}}\)

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mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{15.6}}}{2}\) = \(\mathtt{\text{7.8}}\)

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r = \(\frac{a+b-c}{2}\) = \(\frac{10+\mathtt{\text{11.9}}-\mathtt{\text{15.6}}}{2}\) = \(\mathtt{\text{3.15}}\)

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P = \(a+b+c\) = \(10+\mathtt{\text{11.9}}+\mathtt{\text{15.6}}\) = \(\mathtt{\text{37.5}}\)