Given: △fkl, fk=a, m∠f=45°, m∠l=30° find: fl

The best way to do this is to draw a picture of ΔFKL and include line segment KM that is perpendicular to FL.  This creates ΔFKM which is a 45°-45°-90° triangle and ΔLKM which is a 30°-60°-90° triangle.

Find the lengths of FM and ML.  Then, FM + ML = FL

FM

ΔFKM (45°-45°-90°): FK is the hypotenuse so FM =

ML

ΔLKM (30°-60°-90°): from ΔFKM, we know that KM = , so KL =  

FM + ML = FL

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