Question

Please help. I don’t know how to work it out and need somebody to show me

Answer 1

Check the picture below.

so hmmm let's firstly convert the angles to degrees only.

so there are 60 minutes in 1 degree, so 10' is really 10/60 = 1/6 of a degree, so 112°10' is really just 112 and 1/6 degrees.

15°20' is just well, 20/60 = 1/3, so that converted to degrees only will be 15 and 1/3 degrees.

now, a triangle has a total of 180° interior angles, so let's get the angle A

`\stackrel{mixed}{112(1)/(6)}\implies \cfrac{112\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{673}{6}} ~\hfill \stackrel{mixed}{15(1)/(3)} \implies \cfrac{15\cdot 3+1}{3} \implies \stackrel{improper}{\cfrac{46}{3}} \\\\[-0.35em] ~\dotfill\\\\ 180-\cfrac{673}{6}-\cfrac{46}{3}\implies \cfrac{105}{2}\implies 52.5^o\impliedby \measuredangle A \\\\[-0.35em] \rule{34em}{0.25pt}`

`\textit{Law of sines} \\\\ \cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\sin(C)}{c}=\cfrac{\sin(A)}{a}\implies \cfrac{\sin((46)/(3)^o)}{c}=\cfrac{\sin(52.5^o)}{354}\implies \cfrac{\sin((46)/(3)^o)}{\sin(52.5^o)}=\cfrac{c}{354} \\\\\\ \cfrac{354\sin((46)/(3)^o)}{\sin(52.5^o)}=c\implies 117.99^o\approx c=AB`

Make sure your calculator is in Degree mode.