Question

4 - nearest minute

5 - nearest second
How to work out a of 4 and a of 5 logically ??? Thanks

Answer 1

4a Answer: 54° 29'

Explanation:

`sin\ \theta=0.814\\\\.\quad \theta=sin^(-1)(0.814)\\\\.\quad \theta = 54.4886\\\\.\quad \theta = 54^o\ +\ (4886)/(10,000)minutes\\\\\\\text{Now, set up the proportion to solve for minutes. 1 degree = 60 minutes}\\\\(4886)/(10,000)=(x)/(60)\\\\x=29.31\ minutes\\\\x=29\ minutes + (31)/(100)\ seconds\\\\\text{since we are solving for minutes and the decimal is less than .5, we do}\\\text{not round up and can disregard the seconds.}`

4a Answer: 26° 33' 54"

Explanation:

`tan\ \theta=0.5\\\\.\quad \theta=tan^(-1)(0.5)\\\\.\quad \theta = 26.565\\\\.\quad \theta = 26^o\ +\ (565)/(1000)minutes\\\\\\\text{Now, set up the proportion to solve for minutes. 1 degree = 60 minutes}\\\\(565)/(1000)=(x)/(60)\\\\x=33.9\ minutes\\\\x=33\ minutes + (9)/(10)\ seconds\\\\\text{Now set up the proportion to solve for seconds. 1 minute = 60 seconds}\\\\(9)/(10)=(x)/(60)\\\\x=54.18\\\\x=54\ seconds\ +\ (18)/(100)`

Since the decimal is less than .5, we do not round up and can disregard the remainder.