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 = 46.5 ° . Find the distance across the lake from A to B.

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!!!