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## Homework Statement

a) Find the speed of the boat with respect to the Earth. (km/h)

b) Find the speed of the boat with respect to the river if the boat's heading in the water is 60° south east (km/h)

## Homework Equations

v(x) = v cos(θ)

v(y) = v sin(θ)

v = √(vx^2+vy^2) but can't use it in here because it is not a right trangle :(

θ = tan^-1 (vy/vx)

## The Attempt at a Solution

I would have easily solved this problem if only I had one unknown. I am completely lost. I barely have any idea on what I am doing. I would love to hear an explanation of each step because I really want to know how to do these sort of problems when the formed triangle isn't a right triangle and when there are two unknowns.

What I have so far is that

V of the boat with respect to the river = V br

V of the boat with respect to the earth = V be

V of river with respect to the earth = V re

V be = V br + V re

V br (x) = ? sin(43) ; V br (y) = ? cos(43)

V be (x) = ? ; V be (y) = ?

V re (x) = 5.4 ; V re (y) = 0

We've never learned this but after researching on the solution I found out how to solve relative motion problems that don't have a right triangle with ijk vector component addition. Another method was also through Law of Sines and Cosines. What I came up with was:

ijk method:

V be = V br + V re

V re = 5.4i; V br = cos(60)i + V br sin(60)j; Vbe = V be cos (43)i + V be sin (43)j

Law of Sines and Cosines method:

V be^2 = V br^2 + V re^2 - 2 * V br * V re * cos 163

This might be incorrect since I barely have any idea about what I am doing. Anyways, even with just plugin it in I still don't know how I can I simplify it to solve it since I still have 2 unknowns.

How can I solve this problem, somebody help D: