Answer :
The area of triangle IJK is 999.8 square centimeters
The given parameters are:
[tex]\angle I = 120^o[/tex]
[tex]\angle J = 59^o[/tex]
[tex]i = 340cm[/tex]
Start by calculating the length of side j using the following sine ratio
[tex]\frac{i}{\sin(I)} = \frac{j}{\sin(J)}[/tex]
Make j the subject of the formula
[tex]j = \sin(J) \times \frac{i}{\sin(I)}[/tex]
Substitute known values
[tex]j = \sin(59) \times \frac{340}{\sin(120)}[/tex]
Evaluate the expression
[tex]j = 337[/tex]
Next, calculate angle K using the following sum of angles formula
[tex]\angle I + \angle J + \angle K =180[/tex]
Substitute known values
[tex]120 + 59 + \angle K =180[/tex]
[tex]179 + \angle K =180[/tex]
Subtract 179 from both sides
[tex]\angle K =1[/tex]
The area of the triangle is:
[tex]Area = \frac{1}{2} ij \times \sin(K)[/tex]
So, we have:
[tex]Area = \frac{1}{2} \times 340 \times 337 \times \sin(1)[/tex]
Evaluate
[tex]Area = 999.8[/tex]
Hence, the area of triangle IJK is 999.8 square centimeters
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