Question
Draw a triangle $ABC$ , with $\mathrm{AC}=4 \mathrm{~cm}, \mathrm{BC}=3 \mathrm{~cm}$ and $\angle C=105^{\circ}$. Measure AB . Is. $(\mathrm{AB})^2=(\mathrm{AC})^2+$ $(B C)^2$ ? If not which one of the following is true:
$(A B)^2>(A C)^2+(B C)^2 \text { or }(A B)^2<(A C)^2+(B C)^2$

Answer


Draw $\triangle \mathrm{ABC}$,
Draw a line $B C=3 \mathrm{~cm}$.
At point $C$, draw a line at $105^{\circ}$ angle with $BC$ .
Take an arc of $4\ cm$ from point $C$, which will cut the line at point $A$.
Now, join $A B$, which will be approximately $5.5\ cm$ .
$\mathrm{AC}^2+\mathrm{BC}^2$
$=4^2+3^2$
$=9+16$
$=25$
$A B^2=5.52=30.25$
$A B^2$ not equal to $A C^2+B C^2$
Here,
$\mathrm{AB}^2>\mathrm{AC}^2+\mathrm{BC}^2$

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