Thread: Triangle Trig Question

Last One!

A farmer has a triangular field with sides of 240 ft., 300 ft., and 360 ft. He wants to apply fertilizer to the field. If one 40-pound bag of fertilizer covers 6000 square feet, how many bags must he buy to cover the field.
I drew a diagram and have a feeling I need to use these equations
Law of Cosines
Area of a triangle (1/2 ab sinC)

I just don't know how I would go about it

Originally Posted by ~berserk

Last One!

A farmer has a triangular field with sides of 240 ft., 300 ft., and 360 ft. He wants to apply fertilizer to the field. If one 40-pound bag of fertilizer covers 6000 square feet, how many bags must he buy to cover the field.
I drew a diagram and have a feeling I need to use these equations
Law of Cosines
Area of a triangle (1/2 ab sinC)

I just don't know how I would go about it

Use Cosine rule to get the angle opposite one of the sides.

240^2 = 300^2 + 360^2 - 2*300*360CosA

CosA = (300^2 + 360^2 - 240^2)/(2*300*360)

A = Cos^-1(3/4)

Area = 0.5*300*360Sin(Cos^-1(3/4)) = 35718 sq ft

35718 / 6000 = 5.953

Therefore he needs 6 bags.