4a Answer: 54° 29'
Step-by-step explanation:
[tex]sin\ \theta=0.814\\\\.\quad \theta=sin^{-1}(0.814)\\\\.\quad \theta = 54.4886\\\\.\quad \theta = 54^o\ +\ \dfrac{4886}{10,000}minutes\\\\\\\text{Now, set up the proportion to solve for minutes. 1 degree = 60 minutes}\\\\\dfrac{4886}{10,000}=\dfrac{x}{60}\\\\x=29.31\ minutes\\\\x=29\ minutes + \dfrac{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.}[/tex]
4a Answer: 26° 33' 54"
Step-by-step explanation:
[tex]tan\ \theta=0.5\\\\.\quad \theta=tan^{-1}(0.5)\\\\.\quad \theta = 26.565\\\\.\quad \theta = 26^o\ +\ \dfrac{565}{1000}minutes\\\\\\\text{Now, set up the proportion to solve for minutes. 1 degree = 60 minutes}\\\\\dfrac{565}{1000}=\dfrac{x}{60}\\\\x=33.9\ minutes\\\\x=33\ minutes + \dfrac{9}{10}\ seconds\\\\\text{Now set up the proportion to solve for seconds. 1 minute = 60 seconds}\\\\\dfrac{9}{10}=\dfrac{x}{60}\\\\x=54.18\\\\x=54\ seconds\ +\ \dfrac{18}{100}[/tex]
Since the decimal is less than .5, we do not round up and can disregard the remainder.
