Question

in triangle ABC angle at B AB=24, BC=7 determine cos A​

Answer 1

Step-by-step explanation:

$\bf {\blue{ \underline{Question : }}}$

In triangle ABC angle at B AB=24, BC=7 determine cos A

$\huge{ \boxed{ \bold{ {Given}}}}$

• AB = 24

• BC = 7

$\boxed{ \huge{ \bold{to \: find}}}$

• CosA = ?

$\pink{ \underline{ \underline{Ｓｏｌｕｔｉｏｎ : - }}}$

Using Pythagorean theorem,

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{AB² + BC² = AC²}$

$\: \: \: \: \: \: \: \: \: {\implies{ \sf{ {(24)}^{2} + {(7)}^{2} = {AC}^{2}}}}$

$\: \: \: \: \: \: \: \: \: {\implies{ \sf{ 576 \: + 49= {AC}^{2} }}}$

$\: \: \: \: \: \: \: \: \: {\implies{ \sf{ 625= {AC}^{2} }}}$

$\: \: \: \: \: \: \: \: \: {\implies{ \sf{ \sqrt{625} = {AC }}}}$

$\: \: \: \: \: \: \: \: \: {\implies{ \sf{ \red {25}= AC }}}$

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$\: \: \: \: \: \: \: \: \: Cos(A) = \frac{AB }{ AC}$

$\: \: \: \: \: \: \: \: \: \implies Cos(A) = \frac \red{24} \red{ 25}$

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