Question

Please help! Find theta to the nearest minute.
cos theta=0.6955
The angle is
a. 45 degrees 54'
b. 44 degrees 4'
c. 44 degrees 6'
d. 45 degrees 56'

Answer 1

You need to use the inverse cosine to obtain the angle that yields 0.6955. \[\cos^-1(0.6955) \approx 45.933\]

Since there are 60 minutes to a degree, multiply .933 by 60. Therefore the answer is 45 degrees and 55.98 minutes, or simply 56 minutes.

Answer 2

punch this into scientific calc:
\[\cos^{-1} 0.6995 = 45.9329^{0}\]
subtract the 45 degrees and remain with 0.9329, multiply by 60min and get 55.97 minutes,
so answer:
\[45^{0} 56'\]