Answer:
The distance across the lake from A to B = 690.7 ft
Step-by-step explanation:
Points A and B are separated by a lake. To find the distance between them, a surveyor locates a point C on land such that
∠CAB=46.5∘. He also measures CA as 312 ft and CB as 527 ft. Find the distance between A and B.
Given
A = 46.5°
a = 527 ft
b = 312 ft
To find; c = ?
Using the sine rule
[a/sin A] = [b/sin B] = [c/sin C]
We first obtain angle B, that is, ∠ABC
[a/sin A] = [b/sin B]
[527/sin 46.5°] = [312/sin B]
sin B = 0.4294
B = 25.43°
Note that: The sum of angles in a triangle = 180°
A + B + C = 180°
46.5° + 25.43° + C = 108.07°
C = 108.07°
We then solve for c now,
[b/sin B] = [c/sin C]
[312/sin 25.43°] = [c/sin 108.07°]
c = 690.745 ft
Hope this Helps!!!
