Question

Find the values of the sine, cosine, and tangent for ZA. (TOP OF TRIANGLE IS (A))

Answer 1

$\bigstar\:{\underline{\sf{In\:right\:angled\:triangle\:ABC\::}}}$

• AC = 7 m
• BC = 4 m

⠀⠀⠀

$\bf{\dag}\:{\underline{\frak{By\:using\:Pythagoras\: Theorem,}}}$

$\star\:{\underline{\boxed{\frak{\purple{(Hypotenus)^2 = (Perpendicular)^2 + (Base)^2}}}}}\\\\\\ :\implies\sf (AB)^2 = (AC)^2 + (BC)^2\\\\\\ :\implies\sf (AB)^2 = (AB)^2 = (7)^2 = (4)^2\\\\\\ :\implies\sf (AB)^2 = 49 + 16\\\\\\ :\implies\sf (AB)^2 = 65\\\\\\ :\implies{\underline{\boxed{\pmb{\frak{AB = \sqrt{65}}}}}}\:\bigstar$

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

☆ Now Let's find value of sin A, cos A and tan A,

⠀⠀⠀

• sin A = Perpendicular/Hypotenus = $\sf \dfrac{4}{\sqrt{65}} \times \dfrac{\sqrt{65}}{\sqrt{65}} = \pink{\dfrac{4 \sqrt{65}}{65}}$

⠀⠀⠀

• cos A = Base/Hypotenus = $\sf \dfrac{7}{\sqrt{65}} \times \dfrac{\sqrt{65}}{\sqrt{65}} = \pink{\dfrac{7 \sqrt{65}}{65}}$

⠀⠀⠀

• tan A = Perpendicular/Base = ${\sf{\pink{\dfrac{4}{7}}}}$

⠀⠀⠀

$\therefore\:{\underline{\sf{Hence,\: {\pmb{Option\:A)}}\:{\sf{is\:correct}}.}}}$