In a ABC , B =35^ and C =55^ . Write which of the following is true: 1. A C^2=A B^2+B C^2 2. A B^2=B C^2+A C^2 3. B C^2=A B^2+A C^2

In , = 35^ and = 55^ = 180^ -( + ) = 180^ -(35^ + 55^ ) = 180^ -90^ = 90^ By Pythagoras Theorem, BC^2=AB^2+ AC^2 (iii) is true.

In a ABC , B =35^ and C =55^ . Write which of the following is tr…

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Question

In a $\triangle ABC , \angle B =35^{\circ}$ and $\angle C =55^{\circ}$. Write which of the following is true:

$A C^2=A B^2+B C^2$
$A B^2=B C^2+A C^2$
$B C^2=A B^2+A C^2$

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Answer

In $\triangle\text{ABC}, $
$\angle\text{B}= 35^\circ$ and $\angle\text{C}= 55^\circ$
$\Rightarrow\angle\text{A}= 180^\circ-(\angle\text{B} + \angle\text{C})$
$\Rightarrow\angle\text{A}= 180^\circ-(35^\circ + 55^\circ)$
$\Rightarrow\angle\text{A}= 180^\circ-90^\circ$
$\angle\text{A}= 90^\circ$
By Pythagoras Theorem,
$BC^2=AB^2+ AC^2$
(iii) is true.

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