The boat sails across the river 50 m wide. The boat is carried along the river at an angle of 30º to the shore.

The boat sails across the river 50 m wide. The boat is carried along the river at an angle of 30º to the shore. Determine the resulting boat movement from shore to shore.

Given:

L = 50 meters – the width of the river across which the boat is sailing;

a = 30 degrees – the angle at which the boat is swept away by the current of the river.

It is required to determine S (meter) – the resulting movement of the boat from shore to shore.

According to the condition of the problem, the boat floats across the river, that is, perpendicular to the bank. Then, the resulting movement of the boat will be the hypotenuse of a right-angled triangle, one of the legs of which is the width of the river. From the Pythagorean theorem:

S = L / cos (a) = 50 / cos (30) = 50 / 0.87 = 57.5 meters (the result has been rounded to one decimal place).

Answer: the movement of the boat is 57.5 meters.