Can you help me solve this problem

Question

Two holes are to be drilled 42 and 3/4 inches apart. If they are spaced 20 and 1/2 inches apart horizontally and 37 and 1/2 vertically use trigonometry to find angle a round to one decimal place

Answer 1

What are the two sides of the angle a?  Also, with the given information, the distance between the holes comes out to

d = √(20.5^2 + 37.5^2) ≅ 42.74 inches

which is just slightly lower than the stated distance of 42.75 inches

 

Assuming the stated horizontal and vertical distances are correct, then angle a could be either

 

a = tan^-1(20.5/37.5) ≅ 28.7°

 

or 

 

a = tan^-1(37.5/20.5) ≅ 61.3°

 

 

But without a more complete description (or a link to a picture), we cannot tell which angle is a.

 

Answer 2

The three lengths form a right angle triangle with 42 and 3/4 being the hypotenuse.

The tangent of one  acute angle of the triangle is 37.5/20.5  and the tangent of the other acute angle is 20.5/37.5

I'm not sure which of these angles you require but you can find it using the arctan of the correct tangent.