Points A and B are separated by a lake. To find the distance between them, a surveyor locates a point C on land such than ∠ C A B = 47.4 ° . Find the distance across the lake from A to B.

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!!!

c. (3,2,6) is the answer.