Respuesta :

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 )

Eliza3038269

Hi :)

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            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 :

  • adj. side = 48 (adjacent to the angle)
  • hyp. k (the one we need)

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]

:)

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