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8 ft

Step-by-step explanation:

From the diagram in the file attached, we are drawing a line from the point F horizontally

Let the angle between the line FG and the horizontal line drawn be β

The point of intersection of the vertical line from G and the drawn horizontal line be A

The point of intersection of the vertical line from H and the drawn horizontal line be B

Distance between the points A and G be x ft

From the ΔFGA

tanβ = x ft÷12 inch

         = x (∵ 1 ft = 12 inches)

From the ΔFHB

tanβ = 6 ft ÷ (12 inch + 2 ft)

        = 2

By comparing the tanβ values obtained from both the triangles

x = 2 ft

∴ Height, in feet, of the beam that ends at point G = 6 + 2 =8 ft

step-by-step explanation:

c. (3,2,6) is the answer.