In a 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? . a) 6.82. b)5.66. c)4.74. d)4.24. e)3.89.

D^2 = p^2 + q^2  - 2 pq cos D

d^2 = (4.24)^2 + (4.24)^2  - 2. (4.24) (4.24) cos 68

d^2 = 2 (4.24)^2 -  2. (4.24) (4.24) cos 68

d = 4.74

so the answer will be letter. C

hope this helps

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

Magma  is composed of molten rock and is  stored  in the earth's crust. lava is  magma  that reaches the surface of our planet through a volcano vent.