Question

$85.12°\mathrm{in}\mathrm{degree}\mathrm{decimal}\mathrm{system}\mathrm{can}\mathrm{be}\mathrm{expressed}\mathrm{in}\mathrm{sexagesimal}\mathrm{system}\mathrm{as}:$

• A. $85°7\text{'}15\text{'}\text{'}$
• B. $85°8\text{'}12\text{'}\text{'}$
• C. $85°7\text{'}12\text{'}\text{'}$
• D. $85°8\text{'}15\text{'}\text{'}$

Answer 1

The correct option is C $85°7\text{'}12\text{'}\text{'}$

Here $85.12°$ can be expressed as
$85.12°=85°+(0.12)°\Rightarrow 85.12°=85°+(0.12\times 60)\text{'}\left(\mathrm{since}1°=60\text{'}\right]\Rightarrow 85.12°=85°+7.2\text{'}\Rightarrow 85.12°=85°+7\text{'}+(0.2)\text{'}\Rightarrow 85.12°=85°+7\text{'}+(0.2\times 60)"\left(\mathrm{since}1\text{'}=60\text{'}\text{'}\right]\Rightarrow 85.12°=85°+7\text{'}+12"\Rightarrow 85.12°=85°7\text{'}12\text{'}\text{'}$
Hence $85.12°=85°7\text{'}12"$
in sexagesimal system.