Louise is a naturalist Sine and Cosine Law?

Question

Louise is a naturalist studing the effect of acid rain on fish populations in different lakes. As part of her research , she needs to know the length of Lake Lebarge. Louise makes the measurements shown. how long is the lake

52 degrees ,340 m and 32 degrees

Answer 1

I'm a math teacher, not a naturalist! :-)

If the measurements made are in order,
then angle A measures 52°,
side b = 340m, and
angle C measures 32°.

Because the sum of the measures of the angles of a triangle is 180°,
angle B measures 98°.

From the Law of Sines,
sin(98°) / 340 = sin(52°) / a
a = 340 · sin(52°) / sin(98°)
a = 340(0.78801) / (0.990268)
a = 270.5567 meters

sin(98°) / 340 = sin(32°) / b
b = 340 · sin(32°) / sin(98°)
b = 340(0.52992) / (0.990268)
b = 181.9432 meters

If the measurements are not in order, the 340 meters would be opposite a different angle than the 98° one, and the Law of Sines would yield different results.

Answer 2

What did she measure? I think Lake Lebarge is 17 miles long, at least the one in Saskatchewan.