See photo. based on the diagram, all of the following are true
a) cos38 = 24/x
b) sin52 = 24/x
c) cos38 = x/34
d) cos52 = x/24

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

----> The cosine of angle of 52 degrees is equal to divide the adjacent side to angle of 52 degrees by the hypotenuse