A surveyor measure the distance across a straight river by the following methods:starting across from a tree on the opposite bank. she walks...

In this problem three points - that is the position of the
tree (A), the original position of the surveyor (B), and the position of surveyor after
walking 278 m (C) forms a right angle triangle with angle ABC being a right
angle.

We know the length BC (278 m) and angle BCA (44.7
degrees).

We have to find distance betewwn tree and
original position of surveyor. This is equal to AB

tan(BCA)
= tan(44.7) = (AB)/(BC)

Substituting value of tan 44.7 as
0.9896 and given value of BC:

0.9896 =
(AB)/278

Therefore:

AB =
0.9896*278 = 275.1088
m

Answer:

The river is
275.1088 m wide.