Question

1. 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.

a.) 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.)
b.) Use the Law of Sines to find the measure of T. (Show the appropriate formula, substitutions, and work. Give the measure of T to the nearest degree.)
c.) Find the mF.

Answer 1

a. We are asked to determine the length of side FT, we are given with the sides adjacent to its opposite angle. Therefore, we use the law of Cosine.
                                (FT)² = (FS)² + (ST)² - 2(FS)(ST)(cos 25°)
Substituting the known values,
                           (FT)² = (25 m)² + (55m)² - 2(25 m)(55 m)(cos 25°)
                                   FT² = 1157.6535 m ;  FT = 34.02 m

b. Using Law of Sines,
                           FT / sin 25° = FS / sin x°
Substituting,
                            34.02 / sin 25° = 25 / sin x°
The value of x from the equation above is 18.10°

c. The sum of the angles of a triangle is 180°
                       180° = 25° + 18.10° + mF
                                        mF = 136.9°