If the problem is correct as posted, the the answer given by the book is wrong. Books, like people, are not perfect.Originally Posted by c_323_h
Although the title of your posting here is Law of Sines, the solution of the problem will not even use any sine function. The Law of Sines will give only the other two sides of the triangle, which are not the distance across the canyon. This distance accross the canyon is the distance from corner C to side AB, such that this said distance is perpendicular to AB. Or, this distance is the altitude of the triangle if AB were the base.
Let d = this distance, in yards.
And point D be the intersection of d and AB.
In right triangle ADC,
hypotenuse = AC
one leg = d
the other leg is unknown, = say, x.
angle opposite d is 68deg
tan(68deg) = d/x
x = d/tan(68deg) --------(i)
In right triangle BDC,
hypotenuse = BC
one leg = d also
the other leg is (85-x).
angle opposite d is 75deg
tan(75deg) = d/(85-x)
85-x = d/tan(75deg) --------(ii)
(i) plus (ii),
85 = d/tan(68deg) +d/tan(75deg)
85 = d[1/tan(68deg) +1/tan(75deg)]
d = 85/[1/tan(68deg) +1/tan(75deg)]
d = 85/[0.671975418]
d = 126.49 yards ----------------answer.