Расчет прямоугольного треугольника с катетом b=170 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.
Ответ:
\(a=\mathtt{\text{143}}\)
\(b=170\)
\(c=\mathtt{\text{222}}\)
\(40\)°
\(\mathtt{\text{50}}\)°
h=\(\mathtt{\text{109}}\)
mc=\(\mathtt{\text{111}}\)
Гипотенуза c:
c = \(\frac{b}{\cos{α°}}\) = \(\frac{170}{\cos{(40°})}\) = \(\mathtt{\text{222}}\)Угол β°:
β° = \(90°-α°\) = \(90°-40°\) = \(\mathtt{\text{50}}°\)Высота h:
h = \(b·\sin{α°}\) = \(170·\sin{(40°)}\) = \(\mathtt{\text{109}}\)Катет a:
a = \(\sqrt{c^2 - b^2}\) = \(\sqrt{\mathtt{\text{222}}^2 -170^2}\) = \(\sqrt{49284-28900}\) = \(\sqrt{20384}\) = \(\mathtt{\text{143}}\)или:
a = \(h·\frac{c}{b}\) =\(\mathtt{\text{109}}·\frac{\mathtt{\text{222}}}{170}\) = \(\mathtt{\text{142}}\)или:
a = \(c·\sin{α°}\) = \(\mathtt{\text{222}}·\sin{(40°)}\) = \(\mathtt{\text{143}}\)или:
a = \(c·\cos{β°}\) = \(\mathtt{\text{222}}·\cos{(50°)}\) = \(\mathtt{\text{143}}\)или:
a = \(\frac{h}{cos{α°}}\) = \(\frac{\mathtt{\text{109}}}{cos{(40°)}}\) = \(\mathtt{\text{142}}\)или:
a = \(\frac{h}{sin{β°}}\) = \(\frac{(\mathtt{\text{109}})}{sin{(\mathtt{\text{50}}°)}}\) = \(\mathtt{\text{142}}\)или:
a = \(\sqrt{\frac{c^2 + \sqrt{c^4-4·c^2·h^2}}{2}}\) = \(\sqrt{\frac{\mathtt{\text{222}}^2 + \sqrt{\mathtt{\text{222}}^4-4·\mathtt{\text{222}}^2·109^2}}{2}}\) = \(\sqrt{\frac{49284+\sqrt{86739840}}{2}}\) = \(\sqrt{2.93 \cdot 10^{4}}\) = \(\mathtt{\text{171}}\)Площадь S:
S = \(\frac{hc}{2}\) = \(\frac{\mathtt{\text{109}}·\mathtt{\text{222}}}{2}\) = \(\mathtt{\text{1.21e+04}}\)Радиус описанной окружности R:
R = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{222}}}{2}\) = \(\mathtt{\text{111}}\)Медиана Mc:
mc = \(\frac{c}{2}\) = \(\frac{\mathtt{\text{222}}}{2}\) = \(\mathtt{\text{111}}\)Радиус вписанной окружности r:
r = \(\frac{a+b-c}{2}\) = \(\frac{\mathtt{\text{143}}+170-\mathtt{\text{222}}}{2}\) = \(\mathtt{\text{45.5}}\)Периметр P:
P = \(a+b+c\) = \(\mathtt{\text{143}}+170+\mathtt{\text{222}}\) = \(\mathtt{\text{535}}\)
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