Answer:
cos(A)=sin(26.57°)=0.447
Step-by-step explanation:
we know that
In the right triangle ABC
The angle A and the angle C are complementary angles
so
∠A+∠C=90°
therefore
cos(A)=sin(C) -------> by complementary angles
we have
C=26.57°
sin(26.57°)= 0.447
Hence
cos(A)=sin(26.57°)=0.447
Alternative Method
In the right triangle BDC
[tex]sin(C)=\frac{BD}{BC}[/tex]
Find BD applying Pythagoras Theorem
[tex]BD^{2}=BC^{2} -DC^{2}[/tex]
substitute the values
[tex]BD^{2}=17.89^{2} -16^{2}[/tex]
[tex]BD^{2}=64.0521[/tex]
[tex]BD=8\ units[/tex]
substitute the values
[tex]sin(C)=\frac{8}{17.89}=0.447[/tex]
[tex]cos(A)=sin(C)=0.447[/tex]
