Two triangles with the same angles 75 degrees, 54 degrees, and 54 degrees triangle ABC has length of 16 and 17 triangle DEF has one length of 45 and one side of = x solve x
In triangle ABC, the length of side AB = 16, and the length of side AC = 17, with angles A = 75°, B = 54°, and C = 54°.
In triangle DEF, we need to solve for the length of side EF, denoted as x. We also know that angles D = 75°, E = 54°, and F = 54°.
Since both triangles have the same angles, they are similar triangles.
By the proportionality of sides in similar triangles, we can set up the following ratios:
AB/DE = AC/EF = BC/DF
16/x = 17/45
Cross multiply:
16 * 45 = 17 * x
720 = 17x
Divide by 17 on both sides:
720/17 = x
x ≈ 42.35
Therefore, the length of side EF in triangle DEF is approximately 42.35 units.