Trigo word problem

Question

A television station uses a helicopter and takes aerial photos of the traffic along a busy road busy in Magsaysay Avenue. During one particular day, the angle of depression of the helicopter to the left end of the traffic jam is 44.5 degrees with a slant distance of 1500 m. The angle of depression to the right end of the jam is found to be 56.8 degrees. What is the length of the traffic jam on that on that particular morning?

Answer 1

Draw a diagram.  Let's say that the helicopter is located at point H, the point on the ground at the left end of the traffic jam is A, the point on the ground at the right end of the traffic jam is B, and the point on the ground directly below H is C. Draw the diagram so that B is closer to C than A.  Let x be the length of the traffic jam (the distance from A to B).    

 

Then, ∠HAB=44.5°, ∠HBC=56.8°, ∠HBA=180°-56.8°=123.2°, and       ∠BHA=180°-123.2°-44.5°=12.3°   

 

By the Law of Sines, (sin123.2°)/1500 = (sin12.3°)/x

 

So, x(sin123.2°) = 1500(sin12.3°)

 

                    x ≈ 382 meters