Answer:
[tex]\cos(\theta)=\frac{4}{5}[/tex]
Step-by-step explanation:
Step 1:
Let us find the missing side. We know this is a right triangle, so we can use the pythagorean thereom to find the last side. Let us set 12 as variable a, 20 as variable c, and the unknown side as variable b.
[tex]a^2+b^2=c^2\\12^2_b^2=20^2\\b^2=400-144\\b^2=256\\b=\pm16[/tex]
We do know that a length can never be negative, so the side b would be 16.
Step 2:
According to SOHCAHTOA, cosine is utilizes the adjacent and hypotenuse of the given angle theta. Let us write the equation:
[tex]\cos(\theta)=\frac{adjacent}{hypotenuse} \\\\\cos(\theta)=\frac{16}{20} \\\\\cos(\theta)=\frac{4}{5}[/tex]
I hope this helps! Let me know if you have any questions :)
