What is the approximate value of cos 31º14'? (Use a table and interpolation)?

Question

a 0.8563 b 0.8551 c 0.5185 d 0.5165

I did the formula in the book but got nothing like these , Help

Answer 1

You use a table, I'll use a calculator.

31º14' = 31.233 deg

Cos 31.233 = 0.8550627

B

but to try the interpolation

31º10' = 0.8557

31º20' = 0.8557

woops, can't be correct, both the same

Should be

31º10' = 0.8557

31º20' = 0.8542

difference is .0015

this if for 10', so for 4', the difference value would be

4/10 * 0.0015 or 0.0006

subtract this from the lower value

31º14' = 0.8557 - 0.0006 = 0.8551

or B

Note that values go down as angle goes up, so you subtract instead of add.

.

Answer 2

what formula is in the book?

btw, the answer is B

Answer 3

cos 31º=.8571

cos 32º=.8480

cos 31º14' is 14/60ths between cos 31º and cos 32º

Take (.8571-.8480) and multiply by 14/60:

.0091*(14/60)=.0021

Then subtract that from .8571 to get .8550.  Choose answer b and call it a rounding error.

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