Given the triangle:
To find the length of the missing side, considering that you know the measure of the opposite angle to the side and the length of the other two sides, you can apply the cosine law, which is:
[tex]c^2=a^2+b^2−2ab*cosC[/tex]
Consider
a= 245yd
b=270yd
c= x yd
∠C=70º
Replace the values in the formula:
[tex]\begin{gathered} c^2=a^2+b^2-2ab*cosC \\ c^2=245^2+270^2-2*245*270*cos70 \\ c^2=60025+72900-132300*cos70 \\ c^2=132925-132300*cos70 \\ c^2=87675.73504 \\ \sqrt{c^2}=\sqrt{87675.73504} \\ c=296.1yd \end{gathered}[/tex]
The length of the lake is 296yards
