Question 411721
given:

{{{a=24in}}}
{{{b=46in}}}

first find hypothenuse {{{c}}}... use Pythagorean Theorem

{{{c=sqrt(24^2+46^2)}}}

{{{c=sqrt(576+2116)}}}

{{{c=sqrt(2692)}}}

{{{c=51.9}}}


use Trigonometric Identities to find angles:


{{{sin(A) = a / c}}} 


{{{sin(A) = 24 / 51.9 }}}


{{{sin(A) = 0.46}}}


{{{A = 0.48}}}radians


{{{A = 27.39}}} degrees



{{{sin(A)/a = sin(B)/b}}}.....solve for {{{sin(B)}}}



{{{.46/24 = sin(B)/46}}}



{{{(.46/24)46 = sin(B)}}}


{{{0.8817 = sin(B)}}}


{{{B=1.0758622}}} radians


{{{B=61.642365}}} degrees