Answer:
476 feet
Step-by-step explanation:
The given problem when graphically depicted forms a right triangle which has been attached below.
We want to determine the distance between Runner A and Runner B in the diagram.
Using Trigonometric Ratios
In Right Triangle AHC
[tex]\tan 38^\circ =\dfrac{1700}{AC} \\$Cross multiply$\\AC *\tan 38^\circ =1700\\AC =\dfrac{1700}{\tan 38^\circ}\\\\=2175.9$ feet[/tex]
In Right Triangle BHC
[tex]\tan 45^\circ =\dfrac{1700}{BC} \\$Cross multiply$\\BC *\tan 45^\circ =1700\\BC =\dfrac{1700}{\tan 45^\circ}\\\\=1700$ feet[/tex]
The distance between the two runners,
AB=AC-BC
=2175.9-1700
=475.9
=476 feet ( to the nearest foot)
