Question

${114.59}^{\circ }$ can be written in terms of degrees, minutes and seconds as

• A. ${114}^{\circ }{35}^{\prime }{24}^{\prime \prime }$
• B. ${112}^{\circ }{35}^{\prime }$
• C. ${115}^{\circ }{24}^{\prime }{35}^{\prime \prime }$

Answer 1

The correct option is A ${114}^{\circ }{35}^{\prime }{24}^{\prime \prime }$

Given angle as ${114.59}^{\circ }$ which can be written as:
${114.59}^{\circ }={114}^{\circ }+{0.59}^{\circ }$
Now, $1^{\circ }={60}^{\prime }\Rightarrow {0.59}^{\circ }={0.59}^{\circ }\times {60}^{\prime }$
$\Rightarrow {0.59}^{\circ }={35.4}^{\prime }={35}^{\prime }+{0.4}^{\prime }$
Also, $1^{\prime }={60}^{\prime \prime }\Rightarrow {0.4}^{\prime }=0.4\times 60={24}^{\prime \prime }$
$\Rightarrow {114.59}^{\circ }={114}^{\circ }{35}^{\prime }{24}^{\prime \prime }$