SOLUTION: A ship is anchored off a long straight shoreline that runs north and south. From two observation points 18 miles apart on shore, the bearings of the ship are N 37° E and S 55° E.

Question 1135714: A ship is anchored off a long straight shoreline that runs north and south. From two observation points 18 miles apart on shore, the bearings of the ship are N 37° E and S 55° E. What is the distance from the ship to each of the observation points? (Round your answers to one decimal place.)
distance from northern point
= mi
distance from southern point
= mi

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
a triangle is formed.

the triangle is labeled ABC.

A is the intersection of 2 lines created from B and C.

the length of line BC is equal to 18 miles.

angle C is the south end of the line BC, whose angle is north 37 degrees east.

aangle B is the north end of the line BC, whose angle is south 55 degrees east.

the triangle formed is ABC.

since the sum of the angles of a triangle is 180 degrees, then angle A must be equal to 180 - 37 - 55 = 88.

once you have this down, then you can use the law of sines to find the length of AC and the length of AB.

your formula is a / sin(A) = b / sin(B) = c / sin(C).

a is the side opposite angle A.
b is the side opposite angle B.
c is the side opposite angel C.

a/sin(A) is equal to 18 / sin(88) which is equal to 18.0109718.

a / sin(A) becomes 18.0109718.

\the formula becomes 18.109718 = b / sin(B) = c / sin(C).

solve for b to get b = sin(B) * 18.109718.
since B = 55 degrees, then b = sin(55) * 18.109718 = 14.75372437 miles.

solve for c to get c = sin(C) * 18.109718.
since C = 37 degrees), then c = sin(37) * 18.109718 = 10.83927341 miles.

your solution should be that the distance from the northern point = c = 10.8 miles and the distance from the southern point = b = 14.8 miles.

here's what my diagram looks like.

$$$

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