Too many tutors don't "tute" enough.  Mostly they just hand out answers.
I think a tutor should be a teacher, not an answer-giver.

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In right triangle LMN, ∠N is a right angle and cos M = 46/85. What is m∠L to the nearest degree?
In a right triangle, the two acute angles M and L are COmplementary.

Notice that "complementary" begins with the prefix "CO". 

WThe side that is ADJACENT to one acute angle is OPPOSITE to the other.

Therefore:

The sine of one acute angle is the COsine of the other.
The tangent of one acute angle is the COtangent of the other.
The secant of one acute angle is the COsecant of the other.

Just as "COmplement" starts with CO, so do COsine, COtangent,
and COsecant.

"COsine" is short for "COmplement's sine".
"COtangent" is short for "COmplement's tangent".
"COsecant" is short for "COmplement's secant".

So the M's COSINE is L's SINE.  

That is, cos(M) = sin(L) = 46/85
 
On your TI calculator get 

sin-1(46/85)

Read 32.76376226 

Answer: 33°

Edwin
 

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