Question

Points A and B are separated by an obstacle. In order to find the distance between them, a third point C is selected which is 120 yards from A and 150 yards from B. The angle ABC to BAC = 80° 10'. Find the distance from A to B.

Answer 1

The distance from A to B can be calculated using the Law of Cosines, given the lengths from A to C and B to C, and the angle between them. The distance AB is approximately 175.07 yards.

Step-by-step explanation:

To find the distance from A to B given an obstacle, we can use the Law of Cosines in trigonometry with the given points A, B, and C, forming a triangle. The Law of Cosines relates the lengths of sides of a triangle to the cosine of one of its angles:

AB2 = AC2 + BC2 - 2(AC)(BC)cos(∠ACB)

With the given lengths AC = 120 yards, BC = 150 yards, and the angle ∠ACB = 80° 10', we plug these values into the equation and solve for AB.

First, convert the angle to decimal form: ∠ACB = 80 + 10/60 = 80.1667°. Next, calculate AB using the formula:

AB2 = 1202 + 1502 - 2(120)(150)cos(80.1667°)
= 14400 + 22500 - 2(120)(150)cos(80.1667°)
= 36900 - 36000cos(80.1667°)
= 36900 - 36000(0.173648)
= 36900 - 6251.7
= 30648.3

Therefore, AB = √30648.3 = approximately 175.07 yards.