Answer:
Option D) cos52 = x/24
Step-by-step explanation:
In this problem angle of 38 degrees and angle of 52 degrees are complementary angles
so
38°+52°=90°
therefore
cos(38°)=sin(52°)
we know that
see the attached figure with letters to better understand the problem
In the triangle ABD
cos(38°)=24/x ----> The cosine of angle of 38 degrees is equal to divide the adjacent side to angle of 38 degrees by the hypotenuse
Remember that
cos(38°)=sin(52°)
so
sin(52°)=24/x
In the right triangle ABC
cos(38°)=x/34 ----> The cosine of angle of 38 degrees is equal to divide the adjacent side to angle of 38 degrees by the hypotenuse
In the right triangle ABD
Applying the Pythagoras Theorem
[tex]BD=\sqrt{x^{2}-576}\ units[/tex]
[tex]cos(52\°)=(\sqrt{x^{2}-576})/x[/tex]----> The cosine of angle of 52 degrees is equal to divide the adjacent side to angle of 52 degrees by the hypotenuse
