Question

A surveyor is shooting a line to a point on a tree 55 m from his current position. After rotating his surveying instrument 25" to the left, he shoots another line to a point on a fence post 25 m away.
Determine the distance between the point on the tree to the point on the fence post. ( show the appropriate formula , substitutions, and work. Give the distance to the nearest hundredth of a meter)

Answer 1

Take a look at the diagram below.
This problem looks like a great candidate for using the Law of Cosines.
If you know two sides, you can find the third side from the angle opposite or vice versa. Should the sides be a, b, and c, and their opp. angles A, B, and C...
a² + b² - 2ab(cosC) = c²

Let's plug in what we know...a = 55, b = 25, and m<C = 25".

55² + 25² - 2(55)(25)(cos(25")) = c²

One thing to note is that our angle measure is in <em />seconds. Unless you're using Google's built in calculator, you'll wind up having to convert to degrees. 60 seconds in a minute, 60 minutes in a degree...blahblahblah.
Anyways, cos(25") comes out to be practically 1. (0.99999993)
Let's get evaluating.

3025 + 625 - 2750(1) = c²
3025 + 625 - 2750 = c²
900 = c²
30 = c

The tree is 30 meters from the fence post.