MATH SOLVE

4 months ago

Q:
# Timelimit: 15 minutes. 11:08 remaining, x A radio tower is located 250 feet from a building. From a window in the building, a person determines that the angle of elevation to the top of the tower is 38 and that the angle of depression to the bottom of the tower is 27. How tall is the tower? Preview feet Points possible: 1 This is attempt 1 of 1. Submit

Accepted Solution

A:

Answer:The height of tower is 322.7 feet.Step-by-step explanation:Given Distance between a building and tower= 250 feetBCDE is a rectangle .Therefore, we have BC=ED and CD=BE=250 feet In triangle ABE[tex]tan\theta=\frac{perpendicula \; side }{hypotenuse}[/tex][tex]\theta=38^{\circ}[/tex][tex] tan38^{\circ}=\frac{AB}{BE}[/tex] [tex]\frac{AB}{250}=0.781[/tex][tex] AB=0.781\times250[/tex]AB=195.25 feetIn triangle EDC[tex]\theta=27^{\circ}[/tex][tex]tan27^{\circ}=\frac{ED}{CD}[/tex][tex]\frac{ED}{250}=0.509[/tex][tex]ED=250\times0.509[/tex]ED=127.25 feet ED=BC=127.25 feetThe height of tower=AB+BCThe height of tower=195.25+127.25=322.5 feet