Question

Two points A and B are on opposite sides of a building. A surveyor selects a third point C to

place a transit. Point C is 54 feet from point A and 70 feet from point B. The angle ACB is 52º.
How far apart are points A and B?
A) 74.1 ft
B) 111.7 ft
C) 56.2 ft
D) 100.7 ft

Answer 1

Using the Law of Cosines, the distance between points A and B is approximately 74.1 ft.

Step-by-step explanation:

To find the distance between points A and B, we can use the Law of Cosines. The formula is as follows: c^2 = a^2 + b^2 - 2ab*cos(C), where a and b are the known side lengths and C is the angle opposite to the side we want to find.

In this case, a = 54 ft, b = 70 ft, and C = 52°. Plugging these values into the formula, we get c^2 = 54^2 + 70^2 - 2*54*70*cos(52°). Solving for c, we find that c is approximately equal to 74.1 ft.