Question

Communities A,B and C are faced with acurate water problem. The distance between A and B is 5km and that of A and C is 7km, the angle between path AB and Ac is 45 degree . If a well is to be dug for the communities such that it would have equal distance in the path linking each communities. A) indicate by using of sketching the exact place to dug the well. B) measure the distance between communities B and C

Answer 1

B) The distance between communities B and c is 4.95 km.

Explanation:

A) Join communities B and C. Then bisect angles A, B and C to determine the mid point equidistant to the three communities. The point where the three bisectors meet, w, is the exact place to dig the well.

The sketch is in the attachment to this answer.

B) Since we have two sides and an included angle, the cosine rule is applicable to determine a (distance between B and C).

`a^(2)` =
`b^(2)` +
`c^(2)` - 2bc Cos A

b = 7 km, c = 5 km and A =
`45^(o)`. So that;

`a^(2)` =
`7^(2)` +
`5^(2)` - 2(5 x 7) Cos
`45^(o)`

= 49 + 25 - 70 x 0.7071

= 74 - 49.497

= 24.503

⇒ a =
`√(24.503)`

= 4.95

The distance between communities B and c is 4.95 km.