# 勾股定理（直角三角形）计算器

## 解决方案

1. $A = \left(\frac{180 \operatorname{asin}{\left(\frac{3}{5} \right)}}{\pi}\right)^0$

第三个角是$B = 180^0 - \left(A + C\right)$

在我们的例子中， $B = 180^0 - \left(\left(\frac{180 \operatorname{asin}{\left(\frac{3}{5} \right)}}{\pi}\right)^0 + 90^0\right) = \left(\frac{- \pi \left(\frac{180 \operatorname{asin}{\left(\frac{3}{5} \right)}}{\pi} + 90\right) + 180 \pi}{\pi}\right)^0$

面积为$S = \frac{1}{2} a b = \left(\frac{1}{2}\right)\cdot \left(6\right)\cdot \left(8\right) = 24$

周长是$P = a + b + c = 6 + 8 + 10 = 24$

2. $A = \left(\frac{- 180 \operatorname{asin}{\left(\frac{3}{5} \right)} + 180 \pi}{\pi}\right)^0$

第三个角是$B = 180^0 - \left(A + C\right)$

在我们的例子中， $B = 180^0 - \left(\left(\frac{- 180 \operatorname{asin}{\left(\frac{3}{5} \right)} + 180 \pi}{\pi}\right)^0 + 90^0\right) = \left(\frac{- \pi \left(90 + \frac{- 180 \operatorname{asin}{\left(\frac{3}{5} \right)} + 180 \pi}{\pi}\right) + 180 \pi}{\pi}\right)^0$

这种情况是不可能的，因为角度是非正的。

## 回答

$a = 6$A

$b = 8$A

$c = 10$A

$A = \left(\frac{180 \operatorname{asin}{\left(\frac{3}{5} \right)}}{\pi}\right)^0\approx 36.869897645844021^0$A

$B = \left(\frac{- \pi \left(\frac{180 \operatorname{asin}{\left(\frac{3}{5} \right)}}{\pi} + 90\right) + 180 \pi}{\pi}\right)^0\approx 53.130102354155979^0$A

$C = 90^0$A