Question

Determine the value of (tangent of 88 degrees, 22 minutes, and 45 seconds). In this case, minutes are 1/60 of a degree and seconds are 1/3600 of a degree.a. 23.42583649 c. 35.34015106 b. 56.36842561 d. 47.69869523

Answer 1

C.

Explanation:

35.34015106

Answer 2

c. 35.34015106

Explanation:

As with many problems of this nature, you only need to get close to be able to choose the correct answer. 22 minutes 45 seconds is just slightly less than 1/2 degree (30 minutes), so the tangent value will be just slightly less than tan(88.5°) ≈ 38. The appropriate choice is 35.34015106.

If you need confirmation, you can find tan(88°) ≈ 29, so you know the answer will be between 29 and 38.

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The above has to do with strategies for choosing answers on multiple-choice problems. Below, we will work the problem.

The angle is (in degrees) ...

88 + 22/60 +45/3600 = 88 + (22·60 +45)/3600 = 88 +1365/3600

≈ 88.3791666... (repeating) . . . . degrees

A calculator tells you the tangent of that is ...

tan(88.3791666...°) ≈ 35.3401510614

Many calculators will round that to 10 digits, as in the answer above. Others can give a value correct to 32 digits. Spreadsheet values will often be correct to 15 or 16 digits.