Jay is 120 meters from the base of a building and Mary is 40 meters from the base of the building. Jay's angle of elevation when looking at the top of the building is X and Mary's is 2X. What is the height of the building?

tangent=opposite/adjacent, H=height of building

tan(x)=H/120

tan(2x)=H/40

120tan(x)=H

40tan(2x)=H

120tan(x)=40tan(2x)

3tan(x)=tan(2x)

tan(2x)=3tan(x)

tan(2x)=2tan(x)/[1-tan^2(x)]

2tan(x)/[1-tan^2(x)]=3tan(x)

2tan(x)=3tan(x)[1-tan^2(x)]

2=3[1-tan^2(x)]

2/3=1-tan^2(x)

-1/3=-tan^2(x)

1/3=tan^2(x)

find the square root of 1/3

square root of 1/3=0.57735

tan of what angle is 0.57735 from the table of tangents ?

the angle x=30 degrees

tan(30)=H/120

120*0.57735=69.28 meters

2x=60 degrees

tan(60)=H/40

tan(60)=1.7321

40*1.7321=69.28 meters