Question

Two points, A and B, are on opposite sides of a building. A surveyor chooses a third point, C, 80 yd from B and 104 yd from A, with angle ABC measuring 51.2 degrees. How far apart are A and B (to the nearest Yard)?

A) 144 yards
B) 152 yards
C) 136 yards
D) 128 yards

Answer 1

The distance between points A and B is approximately 152 yards.

Step-by-step explanation:

To find the distance between two points A and B, we can use the Law of Cosines. Let's call the distance between A and B as x. We know that B is 80 yards away from point C, and A is 104 yards away from point C. We also know that angle ABC is 51.2 degrees.

Using the Law of Cosines, we can write:

x^2 = 80^2 + 104^2 - 2 * 80 * 104 * cos(51.2)

By simplifying the equation, we find that x is approximately 152 yards.