Question 1204848
At a point A on level ground, the angle of elevation to the top of a shed is 20° . If a person walked 30.0 m away from point A, from the shed, to point B, the angle of elevation decreases by 12°. Find the height of the shed.


 the angle of elevation decreases by 12° It becomes 8 deg

y height of shed
x distance from shed to point A on ground

tan 20 = y/x

tan 8 = y/(x+30)

{{{tan 20/tan 80 = (y/x )/(y/(x+30))}}}\


{{{tan 20/tan 8 = (x+30)/x}}}

tan 20 *x = tan 8 *(x+30)

x tan 20 - xtan8  =30 tan 8


x(tan 20-tan 8)= 30 tan 8

x = 30* tan 8/ (tan 20-tan 8)  

tan 20 = y/x

y= x*tan 20 deg The height of shed

Use calculator  to evaluate

 *[illustration shed_height.png].