Two fire towers are x 35 kilometers apart where tower A is

Two fire towers are x = 35 kilometers apart, where tower A is due west of tower B. A fire is spotted from the towers, and the bearings from A and B are = N 76° E and = N 58° W, respectively (see figure). Find the distance d of the fire from the line segmentAB. (Round your answer to two decimal places.)
d = ? km

Solution

Let the distance d meet AB at D.

Using trig:
AD = d*tan() = d*tan(76 deg)

BD = d*tan() = d*tan(58 deg)

AB = AD + BD
35 km = d*tan(76 deg) + d*tan(58 deg)
35 km = d*[tan(76 deg) + tan(58 deg)]
d = (35 km)/[tan(76 deg) + tan(58 deg)] = 35/4.447 = 7.87 km