Application of trigonometric function in high school mathematics? This paper mainly explains why the RT triangle appears in the angle problem.

1. Because the tower is perpendicular to the horizontal plane, AB is perpendicular to BC and BD.

In RT triangle ABC, BC = ab/tan30 = 10 √ 3m.

In the RT triangle ABD, BD = ab/tan45 = 10m.

Because the angle DBC = 15+75 = 90.

So in BDC of RT triangle, DC = √ [(10 √ 3) 2+10 2] m = 20m.

Therefore, the ship speed is 20m/min.

2. According to the meaning of the question, the angle EBD = 90-75 = 15, and because DC in the RT triangle BDC = 2bd.

So angle BDC = 60, angle BDE =120, bed = 45.

EB=BD*sinBDE/sinBED=5√6m

So 5√6m off the island.