Question

$\huge\tt\fbox\purple{•Question}$
In the given ∆ABC it is given that \angle∠ B = 90° .AB = 24 cm and BC = 7 cm than find the Value of Cos A = ?


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Answer 1

$\star \; {\underline{\boxed{\pmb{\pink{\sf{ \; Given \; :- }}}}}}$

• ∠B = 90°
• AB = 24 cm
• BC = 7 cm

$\star \; {\underline{\boxed{\pmb{\green{\sf{ \; To \; Find \; :- }}}}}}$

• Cos A = ?

$\\ \qquad{\rule{200pt}{2pt}}$

$\star \; {\underline{\boxed{\pmb{\orange{\sf{ \; SolutioN \; :- }}}}}}$

$\dag \; {\underline{\underline{\pmb{\sf{ Calculating \; the \; Value \; of \; AC \; :- }}}}}$

$\begin{gathered} \; \; \; \; \purple\longmapsto \; \; \red{\sf{ {Hypoenuse}^{2} = {Base}^{2} + {Height}^{2} }} \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \; \; \longmapsto \; \; \sf{ AC = \sqrt{ \bigg( {BC} \bigg)^{2} + { \bigg( AB \bigg) }^{2} } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \; \; \longmapsto \; \; \sf{ AC = \sqrt{ {\bigg( 7 \bigg)}^{2} + { \bigg( 24 \bigg)}^{2} } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \; \; \longmapsto \; \; \sf{ AC = \sqrt{ 49 + 576 } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \; \; \longmapsto \; \; \sf{ AC = \sqrt{ 625 } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \; \; \longmapsto \; \; {\underline{\boxed{\orange{\pmb{\sf{ AC_{ \; Hypotenuse} = 25 \; cm }}}}}} \; \bigstar \\ \\ \\ \end{gathered}$

$\dag \; {\underline{\underline{\pmb{\sf{ Calculating \; the \; Value \; of \; Cos \; A \; :- }}}}}$

$\begin{gathered} \; \; \; \; \pink\longrightarrow \; \; \purple{\sf{ Cos \; A = \dfrac{Base}{Hypotenuse} }} \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \; \; \longrightarrow \; \; {\underline{\boxed{\color{darkblue}{\pmb{\sf{ Cos \; A = \dfrac{24}{25} }}}}}} \\ \\ \\ \end{gathered}$

$\therefore \;$ Value of Cos A is 24/25 .

$\\ \qquad{\rule{200pt}{2pt}}$

Answer 2

$\star\;{\underline{\boxed{\pmb{\green{\frak{\;Given\; :-}}}}}}$

• $\angle$B = 90°
• AB = 24 cm
• BC = 7 cm

$\star\;{\underline{\boxed{\pmb{\green{\frak{\;To Find\; :-}}}}}}$

$\Huge\sf\implies$$\large\underline\color{Red}{\sf{Value\:of\:Cos\:A}}$

$\star\;{\underline{\boxed{\pmb{\green{\frak{\; Solution\; :-}}}}}}$

$\huge\rightarrow$ In Right Angled ∆ABC , By using Pythagoras theorem we have ,

$\huge\rightarrow$ $\tt\:\color{Blue}{AC²\:=\:AB²\:+\:BC²}$

$\huge\rightarrow$ $\tt \: (24)² + (7)²$

$\Huge\sf\implies$ $\tt \:576 + 49$

$\star\;{\underline{\boxed{\pmb{\pink{\frak{\;625\; :-}}}}}}$

$\therefore$ AC = +25 cm

$\because$ side cannot be negative

Now ,

$\Huge\sf\implies$$\color{Red}{cosA\:=\: \dfrac{B}{H}}$

$\Huge\sf\implies$ $\dfrac{Ab}{AC}$

$\Huge\sf\implies$ $\dfrac{24}{25}$