A sailboat on a lake sails 90. meters north and then sails 60. meters due east. Compared to its starting position, the new position of the sailboat is show your work

The new position of the sailboat is 108.2 m, at N 53.3° E

Explanation:

From the image uploaded, R is the resultant displacement and it is calculated as;

R² = 90² + 60² (Pythagoras theorem)

R² = 11700

R = √11700

R = 108.2 m

The direction of the boat is given by θ in the image uploaded;

tanθ = opp/adj

tanθ = 90 / 60

tanθ = 1.5

θ = tan⁻¹(1.5)

θ = 53.3°

θ = N 53.3° E

Therefore, the new position of the sailboat is 108.2 m, at N 53.3° E