a.

Trong tam giác vuông ABC:

\(tan\widehat{ACB}=\dfrac{AB}{AC}\Rightarrow AC=AB.tan\widehat{ACB}=30.tan30^0=10\sqrt{3}\left(cm\right)\)

Áp dụng định lý Pitago:

\(BC=\sqrt{AB^2+AC^2}=20\sqrt{3}\left(cm\right)\)

\(\widehat{ABC}=90^0-\widehat{ACB}=60^0\)

b.

Áp dụng định lý Pitago:

\(BC=\sqrt{AB^2+AC^2}=\sqrt{569}\left(cm\right)\)

\(tan\widehat{ABC}=\dfrac{AC}{AB}=\dfrac{13}{20}\Rightarrow\widehat{ABC}\approx33^0\)

\(\widehat{ACB}=90^0-\widehat{ABC}=57^0\)

a. 

$\widehat{C}=90^0-\widehat{B}=90^0-58^0=32^0$

$\cos B=\frac{c}{a}\Rightarrow c=a\cos B=72\cos 58^0=38,15$ (cm)

$\sin B=\frac{b}{a}\Rightarrow b=a\sin B=72\sin 58^0=61,06$ (cm)

b.

$\widehat{C}=90^0-\widehat{B}=90^0-40^0=50^0$

$\sin B=\frac{b}{a}\Rightarrow a=\frac{b}{\sin B}=\frac{20}{\sin 40^0}=31,11^0$

$\tan B=\frac{b}{c}\Rightarrow c=\frac{20}{\tan 40^0}=23,84^0$

c.

$\widehat{B}=90^0-\widehat{C}=90^0-30^0=60^0$

$\tan B=\frac{b}{c}\Rightarrow c=\frac{b}{\tan B}=\frac{15}{\tan 60^0}=5\sqrt{3}$ (cm)

$\sin B=\frac{b}{a}\Rightarrow a=\frac{b}{\sin B}=\frac{15}{\sin 60^0}=10\sqrt{3}$ (cm)

d

$a=\sqrt{b^2+c^2}=\sqrt{21^2+18^2}=3\sqrt{85}$ (cm)

$\tan B=\frac{b}{c}=\frac{21}{18}=\frac{7}{6}$

$\Rightarrow \widehat{B}=49,4^0$

$\widehat{C}=90^0-\widehat{B}=40,6^0$

Bài 2: 

Xét ΔABC có \(\widehat{A}>\widehat{B}>\widehat{C}\)

nên BC>AC>AB

Lời giải:

$S_{ABC}=AH.BC:2=12.20:2=120$ (cm²)

Thông tin A=90 độ không có ý nghĩa gì trong bài.

Diện tích ABC:

S = AH.BC : 2

= 12 . 20 : 2

= 120 (cm²)

mọi người ơi ai bit lm hông chỉ tui zới

                               Giải

       Vì\(\Delta ABC~\Delta DEF\) nên ta có:

                \(\widehat{D}=\widehat{A}=45^o\)

               \(\widehat{E}=\widehat{B}=55^o\)

                \(\widehat{F}=\widehat{C}=\left(180^o-45^o-55^o\right)=80^o\)

      Xét\(\Delta ABC~\Delta DEF\)  có:

  \(\frac{AB}{DE}=\frac{AC}{DF}=\frac{BC}{EF}=\frac{2}{3}\)

\(\Rightarrow DE=\frac{AB.3}{2}=7,5\)

   \(DF=\frac{AC.3}{2}=10,5\)

 #hoktot<3# 

3: 

\(BC=\sqrt{12^2+16^2}=20\left(cm\right)\)

HB=12^2/20=7,2cm

=>HC=20-7,2=12,8cm

\(AD=\dfrac{2\cdot12\cdot16}{12+16}\cdot cos45=\dfrac{48\sqrt{2}}{7}\)

\(HD=\sqrt{AD^2-AH^2}=\dfrac{48}{35}\left(cm\right)\)