Answer:
Part 1) [tex]x=20\°[/tex]
Part 2) 0.3420
Option D. 20;3420
Step-by-step explanation:
step 1
Find the measurement of angle x
we know that
[tex]sin(x)=0.3420[/tex]
Using a calculator
[tex]x=sin^{1}(0.3420)=20\°[/tex]
step 2
Find the angle complementary to angle x
Remember that
If two angles are complementary, then their sum is equal to 90 degrees
Let
y ----> measure of angle complementary to angle x
so
[tex]x+y=90\°[/tex]
we have
[tex]x=20\°[/tex]
substitute
[tex]20\°+y=90\°[/tex]
[tex]y=90\°-20\°=70\°[/tex]
we know that
If two angles are complementary, then the sine of first angle is equal to the cosine of the second angle, or the sine of second angle is equal to the cosine of the first angle
so
if
[tex]x+y=90\°[/tex]
then
cos(y)=sin(x)
substitute
[tex]cos(70\°)=sin(20\°)=0.3420[/tex]
