Fire tower a is x = 27 kilometers due west of tower b. a fire is spotted from the towers, and the bearings from a and b are θ = n 70° e and φ = n 54° w, respectively (see figure). find the distance d of the fire from the line segment ab. (round your answer to two decimal places.)

Hey

Let the distance d meet AB at D. 

Using trig: 
AD = d*cot(θ) = d*cot(13 deg) 

BD = d*cot(ϕ) = d*cot(31 deg) 

So: 
AB = AD + BD 
30 km = d*cot(13 deg) + d*cot(31 deg) 
30 km = d*[cot(13 deg) + cot(31 deg)] 
d = (30 km)/[cot(13 deg) + cot(31 deg)] = 5.0035 km (round as needed).

Hoped That Helped You

The answer is 76° i believe