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Bad White [126]
3 years ago
13

Find the value of A E B C and D please

Mathematics
1 answer:
Nikolay [14]3 years ago
5 0
Looks like you've got 3 lines that are all parallel with one transversal diagonally running down the middle. 
Since all of the other lines are parallel to one another, there are only two different angle combinations to be made by the transversal and one of the other lines, one of which being the given 60º angle. 
The other one is found by subtracting that from 180 since a straight angle measures 180º. 
180 - 60 = 120 
The smaller ones are always 60º, and the larger ones are always 120º. 
That means that a = 60, b = 60, and d = 60 
It also means that c = 120 and e = 120. 
Hope this helps!
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\bigstar\:{\underline{\sf{In\:right\:angled\:triangle\:ABC\::}}}\\\\

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  • 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}}.}}}

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