?

Trigonometry

Free Version

Upgrade subject to access all content

Moderate

Acute Angle, Acute Triangle, Law of Cosines, Surveyor

TRIG-JGWRMC

The Big Q railroad company already has a direct 90 km track from Bay City to Elmwood and another direct 125 km track from Bay City to Sulphur. The people of Elmwood and Sulphur appealed to the railroad to build a direct track between their cities.

When the surveyor sketched a map of the area he found that the line of sight from Bay City to the other two cities created a ${56}^{o}$ angle. See the surveyor’s sketch below.

James Gunnin Created for Albert.io. Copyright 2016. All rights reserved

To the nearest tenth of a kilometer, what was the distance of the proposed new track (Side “a” of the surveyor’s sketch)?

A

$ a=71.11\ km $

B

$ a=161.8\ km $

C

$ a=71.2\ km $

D

$ a=105.6\ km $