trigonometry
posted by bill .
2. two look out situations, which are 25 miles apart along the coast on a northsouth shoreline, spot an approaching yacht. One lookout station measures the direction to the yacht at N33 degrees E, and the other station measures the direction of the yacht at S62 degrees E. How far is the yacht from each lookout station? how far is the yacht from the coast?

make a sketch, label the side across from the 33º angle as x, and the side across the 62º as y.
Using the sine law
x/sin33 = 25/sin85
do y the same way.
draw a perpendicular from the boat to shore, giving you a rightangled triangle, call it h
sin 62 = h/x
h = xsin62, and since we know x ....
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