Here is the first question posed, along with sample solutions. (My part continued below.)

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The answers to the above include, in addition to the correct choice, some key "distractors". Replace "tan" with "sin" above and you obtain answer choice (3). Switch the 69 and 102, and you will get choice (4). Replace 69 with 59 and 102 with 86, and your result is choice (2).

Please take note that should you make one of these errors, you will have a 0% chance for a correct answer, whereas if you randomly make a selection, your chances are 25%.

Also, please recognize that the correct solution to this question begins with careful and accurate reading. The ability to read the question is paramount. The best math student is blinded if they cannot read the question.

During my years in the classroom I many many times discovered students who could do such problems perfectly fine if I read the problem to them, but could not handle it on their own. In constructing tests, care has to be taken in controlling how much of the grade should be dependent on the ability to read, and how much actually is dependent on that ability.

Please take note that a student who has absolutely no knowledge of tangent can solve this problem perfectly should they begin by using the Pythagorean Theorem to find the hypotenuse length, then properly apply either sine or cosine. The phrase "tangent must be used" is mathematically incorrect.

My final note is that to obtain feedback about a student's skills and knowledge, I would never make such a question "multiple choice". This type of question creates easy, but hardly useful, data.