Given:
Triangle LJK.
LJ = 89 in, LK = 28 in and m∠L = 42°
To find:
The length of missing side JK.
Solution:
LJ = k = 89
LK = j = 28
JK = l = ?
Using law of cosine:
[tex]l^{2}=j^{2}+k^{2}-2 jk \cdot \cos L[/tex]
Substitute the given values.
[tex]l^{2}=28^{2}+89^{2}-2 \cdot 28 \cdot 89 \cdot \cos 42^\circ[/tex]
[tex]l^{2}=784+7921-4984 \cdot (0.7)[/tex]
[tex]l^{2}=784+7921-4984 \cdot (0.7431)[/tex]
[tex]l^{2}=784+7921-3703.6[/tex]
[tex]l^{2}=5001.4[/tex]
Taking square root on both sides.
[tex]l=70.7[/tex]
The length of the missing side is 70.7 in.
