Answer:
Distance across the lake from A to B = 686.3 ft
Step-by-step explanation:
The sketch of the description is presented in the attached image.
Using the sine rule
[a/sin A] = [b/sin B] = [c/sin C]
Given
A = 47.4°
a = 527 ft
b = 312 ft
To find; c = ?
We first obtain angle B (∠ABC)
[a/sin A] = [b/sin B]
[527/sin 47.4°] = [312/sin B]
sin B = 0.4358
B = 25.8°
Sum of angles in a triangle = 180°
A + B + C = 180°
47.4° + 25.8° + C = 180°
C = 106.8°
[b/sin B] = [c/sin C]
[312/sin 25.8°] = [c/sin 106.8°]
c = 686.3 ft
Hope this Helps!!!
