Your value of θ is not correct.

Notice that cotθ = 1/tanθ, so the equation becomes:

1/tanθ = 0.876443.

Solving this for tanθ gives:

tanθ = 1/0.876443.

Taking the arctangent of both sides gives one solution to this equation to be:

θ = arctan(1/0.876443).

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This angle is acute, so this is the angle you are wanting (all other solutions to tanθ = 1/0.876443 will be a multiple of π plus this solution, and so are not acute). Getting the approximate value of arctan(1/0.876443) and doing what you did to give the answer in degree, minutes, and seconds will yield the correct answer.

Okay,

cot [(.876443)^-1]= (angle)

REMEMBER cot = 1/tan or tan^-1

Since your finding the cotangent of an ANGLE your equation should be

MAKE SURE YOUR CALCULATOR IS IN DEGREE MODE (press 2nd then MODE then Degree)

tan^-1 [(.876443)^-1]= theta

theta = 48.7672819368 degrees

48 degrees

so

.7672819368 is left over.

.7672819368 x60=46.036916208

.036916208 x3600=132.89

48 46' 133"

Hope this helped and remember degree mode.

Have a great day and take care!

~TeenCessnaPilot