Answer:
The approximate value of (y − x) is [tex]17.12\°[/tex]
Step-by-step explanation:
step 1
Find the measure of angle NML
y=m∠NML
[tex]tan(y)=NL/LM[/tex] ---> opposite side to angle y divided by the adjacent side to angle y
see the attached figure to better understand the problem
substitute the given value
[tex]tan(y)=19.1/14.1[/tex]
[tex]y=tan^{-1}(19.1/14.1)=53.56\°[/tex]
step 2
Find the measure of angle LNM
x=m∠LNM
we know that
[tex]x+y=90\°[/tex] -----> by complementary angles
solve for x
[tex]x+53.56\°=90\°[/tex]
[tex]x=90\°-53.56\°=36.44\°[/tex]
step 3
Find the approximate value of y-x
we have
[tex]y=53.56\°[/tex]
[tex]x=36.44\°[/tex]
so
[tex]y-x=53.56\°-36.44\°=17.12\°[/tex]
