Points A and B 1000 meter apart are plotted on a straight highway running east and west. from A, the bearing of tower C is N32*W and from be, the bearing of C is N64*E. approximate the shortest distance of the tower from the highway.

please explain........

6 answers

The problem can be represented by a triangle with a base equal to 1000 m and
base angles A and B. The 3rd angle is C.

A = 90o-32o = 58o.
B = 90o-64o = 26o.
C = 180-58-26 = 96o.

c/sinC = a/sinA.
1000/sin96 = a/sin58
Multiply bothsides by sin58:
a = 1000*sin58/sin96 = 853 m.

b/sinB = c/sinC.
b/sin26 = 1000/sin96
b = 1000*sin26/sin96 = 441 m.

Side b represents the shortest dist.
from highway to Tower C.
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