Question

Find the value of tan GG rounded to the nearest hundredth, if necessary.
E
F
G
48
14
50

Answer 1

I need the figure to be certain, but the three side lengths 14, 48, 50 form a right triangle (14^2 + 48^2 = 50^2). There are two natural placements for the hypotenuse (50):

- If 50 is the hypotenuse and the two legs meeting at G are 48 (opposite F) and 14 (opposite E), then tan(∠G) = opposite/adjacent = 48/14 = 24/7 ≈ 3.43.

- If instead the legs at G are 48 (adjacent) and 14 (opposite), then tan(∠G) = 14/48 = 7/24 ≈ 0.29.

(If 50 is a side opposite G, then ∠G would be a right angle and tan(∠G) is undefined.)

If you can say which side is between which vertices (e.g. EF = 50, FG = 14, GE = 48), I’ll give the single correct rounded value.