Precalculus word problem

Question

Michelle and Stacey are standing at the coastline 10 miles apart. The coast line is a straight line between them. Both can see the same ship in the water. The angle between the coastline and the line between the ship and Michelle is 35°. The angle between the coast line and the line between the ship and Stacey is 45°. 

How far is the ship from Michelle?

Round to the nearest tenth of a mile. 

1. please show your work as a picture

Answer 1

Triangle MXS...

M is Michelle

S is Stacey

X is the ship

MS=10

angle MSX = 45;

angle SMX = 35

so then angle SXM = 100

MX is distance from Michelle to ship

SX is distance from Stacey to ship

law of signs says:

sin 100 / 10 = sin 45/ MX

MX * sin 100 = sin 45 * 10

MX = sin 45 * 10/ sin100

= 7.1801504306169079695388292868431‬

You can figure out the SX the same way

sin 100/10 = sin 35/SX

SX = sin 35 * 10 / sin 100

SX = 5.8242477742144239582221165934042‬