Question

To find the distance across a​ lake, a surveyor took the measurements shown in the figure. Use these measurements to determine how far it is across the lake.
          
34 degrees
540 yd
A
B
C
a = ?

Answer 1

I can solve it, but I need one detail from the picture that isn’t clear: which angle is 34° (∠A, ∠B, or ∠C), which segment is 540 yd (is that BC?), and which side is labeled a (which two points does it connect)? Could you either upload the figure or tell me:

- which vertex has the 34° angle,
- which two vertices are 540 yd apart,
- which two vertices are the endpoints of the side a?

If you prefer the general method now: label side lengths a = BC (opposite A), b = CA (opposite B), c = AB (opposite C). If BC = 540 and the 34° is angle B, and you want side b (opposite B), use the Law of Sines:

b / sin(B) = 540 / sin(A) → b = 540 · sin(B) / sin(A).

Give the missing label(s) and I will compute the numeric answer.