From the top of a 100 meter bulding the angle of elevation to the top of another building on the opposite side of the street is 25 degrees and angle of depression to the foot of the building is 40 degrees. find the height of the opposite building

If the opposite building  is x m higher than the 100m builder  and y is distance between the 2 buildings we have the equations:-

tan 25  = x / y
tan 40 = 100/y
y = 100 / tan 40 =  119.18

substituting in first equation

tan 25 = x / 119.18

x = 119.18 * tan25 =  55.57 m

So the height of the opposite building = 100 + 55.57 = 155.57 m  answer