Answer:
k ≈ 50.77
Step-by-step explanation:
using the cosine ratio in the right triangle
cos19° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{48}{k}[/tex] ( multiply both sides by k )
k × cos19° = 48 ( divide both sides by cos19° )
k = [tex]\frac{48}{cos19}[/tex] ≈ 50.77 ( to 2 dec. places )
Hi :)
We'll use sohcahtoa to solve this problem
[tex]\Large\boxed{\begin{tabular}{c|1} \sf{Sohcahtoa} ~&~~~~~Formula~~~~~~~ \\ \cline{1-2} \ \sf{Soh} & Opp~\div \text{hyp}\\\sf{Cah} & Adj \div \text{hyp}\\\sf{Toa} & Opp \div \text{adj} \end{tabular}}[/tex]
Looking at our triangle, we can clearly see that we have :
Set up the ratio
[tex]\longrightarrow\darkblue\sf{cos(19)=\dfrac{48}{k}}[/tex]
solve for k
[tex]\longrightarrow\darkblue\sf{k\cos(19)=48}[/tex] > multiply both sides by k to clear the fraction
[tex]\longrightarrow\darkblue\sf{k=\dfrac{48}{\cos(19)}}[/tex] > divide both sides by cos (19)
[tex]\star\longrightarrow\darkblue\sf{k\approx50.77}\star[/tex]
[tex]\tt{Learn~More ; Work\ Harder}[/tex]
:)