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I am having difficulty doing this problem. Any help would be greatly appreciated.

A child walks due east on the deck of a ship at 5 kilometers per hour.

The ship is moving north at a speed of 30 kilometers per hour.

Find the speed and direction of the child relative to the surface of the water.

(a) Speed = __?___ km/h

(b) The angle of the direction is __?__radians.

Note : Traditionally north is 0 degrees so 0 rad, east is 90 degrees so (pi2) rad, south is 180 degrees so pi rad and west is 270 degrees or ((3pi)/2) rad.

(a) Since the speed is the hypotenuse of a right triangle, the answer would be the square root of the sum of the squares of the two sides. That is, it would be sqrt(5²+30²).

That is sqrt(25+900) = sqrt(925) = 30.4.

(b) The angle can be found with the tangent since this is a right triangle.

That is, given it is angle A, tan(A) = 30/5. Since 30/5 6, A = atan(6).

That is the angle with 0 being due east.

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