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2016-03-11T22:33:34+08:00

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Solve the measure of remaining sides using Law of Sines:

Given:  
     Vertex angle = 40 degrees
     Opposite side of vertex  (base)= 4 ft.
     Base angle = 70 degrees  
     Opposite side of base angle (leg) = x

Note: Base angle = (180° - 40°)/2
                               = 140° - 2
                               = 70°

Solution:
  
       4 ft                x
    ------------   =  ---------
     sin 40°          sin 70°
 
     x (sin 40°)  =  4 ft (sin 70°)
   
     x (sin 40°)      4 ft (sin 70°)
   ---------------- =  ------------------
        ( sin 40°)          (sin 40°)
 
           4 ft (0.9377)
    x = --------------------
               0.6428

           3.7588 ft.
    x = -------------
           0.6428
 
    x = 5.85 ft or 6 ft.

ANSWER:  The remaining sides are 6 ft each in measure because legs of an isosceles triangle are congruent.
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