(20 13? Yiyang) As shown in the picture, there is an isolated island in Zishan Lake, Yiyang City, and there is a straight sightseeing trail AB by the lake. Now I decided to build a landscape from the

(20 13? Yiyang) As shown in the picture, there is an isolated island in Zishan Lake, Yiyang City, and there is a straight sightseeing trail AB by the lake. Now I decided to build a landscape from the island. Let PD=x meters,

∵PD⊥AB，

∴∠ADP=∠BDP=90，

In Rt△PAD, tan∠PAD=xAD,

∴AD=xtan38.5 ≈x0.80=54x，

In Rt△PBD, tan∠PBD=xDB.

∴DB=xtan26.5 ≈x0.50=2x，

AB = 80.0m，

∴54x+2x=80.0，

Solution: x≈24.6, that is, PD≈24.6 meters,

∴DB=49.2 meters.

Answer: The small bridge PD is about 24.6 meters long, located between AB and 49.2 meters away from point B. 。