Question 678446
given:

right triangle ABC

< {{{A=35}}} degrees, hypotenuse {{{c=16}}}

to find: {{{a}}} and {{{b}}}


since triangle is right triangle < {{{C=90}}}degrees, and < 

{{{B=90-35=55}}}degrees

use

{{{sin (A) = a/c}}} and {{{sin (B) = b/c}}}


{{{sin B = b/c}}} to find {{{a}}} and {{{b}}}

{{{sin (35) = a/16}}}

{{{sin (35)*16 = a}}}

{{{0.573576*16 = a}}}

{{{highlight(9.177216 = a)}}}


{{{sin (55) = b/16}}}

{{{sin (55)*16 = b}}}

{{{0.819152*16 = b}}}

{{{highlight(13.106432 = b)}}}

now we can use Pythagorean theorem and check our solutions:

{{{c^2=a^2+b^2}}}

{{{16^2=9.177216^2+13.106432 ^2}}}

{{{256=84.221293510656+171.778559770624}}}

{{{256=255.99985328128}}}

{{{256=256}}}