Na laboratory experiment, an ultrasound detector located at d is used to measure the distances of two moving objects, p and q. at a certain moment, p and q are located as shown in the diagram. what is distance pq?

Triangle PDQ has: 

     Side "p" is opposite Angle P 

     Side "d" is opposite Angle D = 45º + 23º = 68º 

     Side "q" is opposite Angle Q 

Use the Law of Cosines: 

         d²  =  p²  +  q²   −   2 • p • q • cos(D) 

         d²  =  (4.24)²  +  (4.24)²   −   2 • (4.24) • (4.24) • cos(68º) 

         d²  =  2(4.24)²   −   2(4.24)² • cos(68º) 

         d²  =  2(4.24)² • [ 1 – cos(68º) ] 

         d  =  4.74 ft
Hope this helps