Final answer:
To approximate cot 16°40' to four decimal places, convert the angle to decimal form and use a calculator to find the reciprocal of tan(16.6667°). The best choice from the given options would be (d) 2.7475.
Step-by-step explanation:
To approximate the cotangent of 16°40' (16 degrees and 40 minutes) to four decimal places using a calculator, you'll need to first convert the angle to decimal form if your calculator requires it. That means you convert 40 minutes to a fraction of a degree by dividing by 60 (since there are 60 minutes in a degree), resulting in approximately 16.6667°. Then you would either directly calculate cot(16.6667°) or calculate the reciprocal of tan(16.6667°), depending on your calculator's functions.
The cotangent of an angle in trigonometry is the ratio of the adjacent side to the opposite side in a right-angled triangle, or, more commonly, the reciprocal of the tangent function (cot(θ) = 1/tan(θ)). It's important to pay attention to the accuracy of the significant figures and approximation rules when performing such calculations.
Based on the options provided and assuming a calculator is used correctly, option (d) 2.7475 would be the most appropriate choice as it is the one close to the actual value of cot(16°40') when approximated to four decimal places.