> Essentially, all you need is two sides and one angle of the triangle, or one side and two angles.

Although you may need the cosine rule rather than the sine rule. The cosine rule is more complicated: it says: sqr(a) = sqr(b) + sqr(c) - 2 bc cos(A).

And I think you need the cosine rule to get home. The sine rule will give you your distance to the landmark. So you can draw a triangle CLH where C is your current location, L is the landmark and H is home, and you know the distance CL and LH and the angle at L. But the sine rule can't help you because the angle you know isn't opposite to any of the sides you know. You have to use cosine rule instead. Which means doing squares, square roots, additions and subtractions as well as memorising the cosine table (or knowing how to derive it from the sine table).

Alternative, you can draw a scale drawing. If you have enough information to do the maths you have enough to draw the triangles, and then you can measure the answer with a ruler.