Please help me solve this problem!

Question

Point A is 200 meters directly east of point B. The bearing from point A to point C is 𝑆 60° 𝑊 and the bearing from B to C is 𝑆 50° 𝐸. Find the distance from A to C to the nearest meter

Answer 1

Create a diagram using the given information to construct triangle ABC. Note that A is due East of B so side AB is horizontal in the plane. The bearings convention used here gives an acute angle E or W of N or S; thus, S 60° W might be read as "60° West of due South." So, the complements of the 2 given angles are the interior angles of this triangle: m < B = 30° and m < A = 40° which means m < C = 110°.

We are given ASA, meaning we know the measures of 2 angles and the measure of the included side, so the triangle's measures are completely determined and we can calculate the remaining measures by using Law of Sines as follows:

sinB / AC = sinC / AB

sin30° / AC = sin110° / 200

AC = 200sin30° / sin110° ≈ 106.42 m