Question

c) In the right - angled A ABC, 2 B = 90°. If |(AC) = 61 cm and length (AB) = 11 cm. Find the
length of Seg BC.
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Answer 1

$\bigstar \: \color{pink} \underline\mathfrak{Given:} \:$

• In Right Angled Triangle ABC , ∠B = 90° , length (AC) = 61cm and length (AB) = 11cm .

$\bigstar \: \color{pink}\underline\mathfrak{To \: find:} \:$

• Length of seg BC = ?

$\bigstar \color{pink}\ \underline\mathfrak {Theorem \: used:} \:$

• Pythagoras theorem - In a right angled triangle the square of its hypotenuse is equal to the sum of square of other two sides.

$\bigstar \: \color{pink}\underline\mathfrak{Solution:} \:$

By Pythagoras theorem ,

$\bf {AC}^{2} = {AB}^{2} + {BC}^{2}$

$: \implies \sf{61}^{2} = {11}^{2} + {BC}^{2}$

$: \implies \sf3721 = 121 + {BC}^{2}$

$: \implies\sf3721 - 121 = {BC}^{2}$

$: \implies \sf 3600 = {BC}^{2}$

$: \implies \sf \fbox{ \purple{60 = BC}}$

Therefore, the length of BC is 60cm .