Question 1206864



Part A: Find cos 

assuming you need to find

{{{cos(X)}}}

using formula {{{cos(X)=adj/hyp }}} 


In triangle {{{XYZ}}}, {{{XY}}} is the adjacent side to angle {{{X}}}, and {{{ZX}}} is the hypotenuse. 

we are given {{{adj=2.5}}} and {{{hyp =5.59}}}

{{{cos(X)=2.5/5.59}}}

{{{cos(X)=0.447}}}

now, compare {{{cos(X) }}}to {{{cos(A) }}}in triangle {{{ABC}}}
 
since {{{ABC}}} is dilated from triangle {{{XYZ}}} by factor {{{2}}}, we know that triangles {{{XYZ}}} and {{{ABC}}} are {{{similar}}}, and corresponding angles  are {{{congruent}}}

so {{{cos(X)=cos(A)=0.447}}}


 
Part B: Find {{{AC}}} and {{{BA}}}. 

Given the scale factor of {{{2}}}, the corresponding sides of triangle {{{ACB}}} are {{{twice}}} the {{{length }}}of triangle {{{XYZ}}}}. 

So,

{{{AC = 2 * XY = 2 *2.5 = 5}}}

{{{BA = 2 *ZX = 2*5.59 = 11.18}}}