In triangle GFD, side GF is 13 cm, angle FDG = 45 degrees, angle DGF is 60 degrees. Find the FD side.
| July 22, 2021 | education
For the solution we use the theorem of sines for triangles.
The ratio of the lengths of the sides of the triangle to the sine of the opposite side of the corner in the triangle is equal, then:
FG / Sin FDG = FD / Sin FGD.
13 / Sin45 = FD / Sin60.
FD = 13 * Sin60 / Sin45.
FD = 13 * (√3 / 2) / (√2 / 2) = 13 * √3 / √2 = 13 * √6 / 2 = 6.5 * √6 cm.
Answer: Side length FD = 6.5 * √6 cm.
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