Question

In a right angled triangle ABC, right angled at B.

AC = 5m, B = 4m, BC =?​

Answer 1

$Given, In \triangle ABC , \angle B = 90\degree,$

$AC = 5\: m \: and \: AB= 4 \: m , BC = ?$

/* By Phythagorean theorem */

$\boxed{ \pink{ AC^{2} = AB^{2} + BC^{2}}}$

$\implies 5^{2} = 4^{2} + BC^{2}$

$\implies 5^{2} - 4^{2} =BC^{2}$

$\implies 25 - 16 =BC^{2}$

$\implies 9=BC^{2}$

$\implies BC = \sqrt{9}$

$\implies BC = 3\:m$

Therefore.,

$\red{BC }\green {= 3\:m }$

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Answer 2

Given :-

• In a right angled triangle ABC, right angled at B. AC = 5m, B = 4m.

To Find :-

• BC

Solution :-

We know that,

$\boxed{\sf AC^{2} = AB^{2} + BC^{2}} \: \: (\bf Pythagoras \: theorem)</p><p>$

Substituting the given values we get,

$:\implies\sf 5^{2} = 4^{2} + BC^{2}$

$:\implies\sf 5^{2} - 4^{2} = BC^{2}$

$:\implies\sf 25 - 16 = BC^{2}$

$:\implies\sf 9 = BC^{2}$

$:\implies\sf\cancel- BC^{2} = \cancel- 9$

$:\implies\sf BC = \sqrt{9}$

$:\implies\underline{\boxed{\blue{\sf BC = 3\:m}}}$

$\green{\therefore\sf BC = 3\:m}$