Đáp án:
Giải thích các bước giải:
\[\begin{array}{l}
a)A{B^2} + A{C^2} = B{C^2}\\
= > ABCvuong\_tai\_A(pytago\_dao)\\
b)Ap\_dung\_he\_thuc\_luong\_trong\_tam\_giac\_vuong\_ABC:\\
\frac{1}{{A{H^2}}} = \frac{1}{{A{B^2}}} + \frac{1}{{A{C^2}}} = > AH = \frac{{48}}{5}\\
\sin B = \frac{{AC}}{{BC}} = \frac{{16}}{{20}} = \frac{4}{5} = > \hat B \approx 53,{13^0} = > \hat C = {90^0} - \hat B = 36,{84^0}\\
C)Ap\_dung\_he\_thuc\_luong\_trong\_tam\_giac\_vuong\_BHA:\\
A{H^2} = AE.AB = HF.AB = > HF = \frac{{192}}{{25}}\\
HE = \sqrt {A{H^2} - H{F^2}} = \frac{{144}}{{25}}\\
d)TanB = \frac{{AC}}{{AB}}\\
SinB = \frac{{AC}}{{BC}}\\
Ma\_ABCvuong\_tai\_A = > BC > AB\\
= > TanB < \sin B
\end{array}\]
