Convert the angle $289{24}^{\text{'}}{15}^{\text{'}\text{'}}$ to decimal form $($show your work$).$

Compute the following bearings to azimuths $($draw a sketch for full credit$)$:

a$.$ S$34{15}^{\text{'}}{20}^{\text{'}}\text{'}$E

b$.N22{34}^{\text{'}}{15}^{\text{'}}\text{'}$ W

Convert the following azimuths to bearings $($draw a sketch for full credit$)$:

a$.67{13}^{\text{'}}{30}^{\text{'}\text{'}}$

b$.346{56}^{\text{'}}{15}^{\text{'}\text{'}}$

Determine back bearing of $S13{16}^{\text{'}}{30}^{\text{'}\text{'}}E($draw a sketch for full credit$)$

Determine the back azimuths of the $146{54}^{\text{'}}{40}^{\text{'}\text{'}}($draw a sketch for full credit$)$

While on your survey far from your office your theodolites rechargeable batteries die on your last measurements of the project. You decide to measure the final angle ABC by chord method. You establish intermediate points D and E both $100\text{'}$ from the origin along the legs of the angle. The chord is then measured to be $52\mathrm{.}76\text{'}.$

a$.$ What is the value of the angle to the nearest minute?

b$.$ To double check your work you've decided to measure the length of the tangent, use the angle you solved for in part a$,$ to back calculate how long your tangent measurement should be $100\text{'}$ from the origin.