Two houses are opposite each other. There are chimneys on both of them. The line joining the chimneys makes an angle 45° with the ground. If the height of one house is 25 m and the height of the other is 10 m, then how far are the houses from each other?

Given:
Height of first house = 25 m
Height of second house = 10 m
Angle of elevation = 45°

Concept:

tan 45° = height/base = BC/AC

Calculation: 
Here, AE = CD = 10 m and AC = ED
So, BC = BD-CD = 25-10 = 15 m

⇒ \(tan 45 = {BC \over AC}\)
⇒ 1 \(= {15 \over AC}\)      [∵  tan 45 = 1]         
⇒ AC = ED = 15 m

∴ The distance between two houses is 15 m.