A girl standing on top of a 25 m building observes a car on the ground at an angle of depression of 45°. Find the distance of the car from the foot of the building.

The girl, the building, and the car form a right-angled triangle.

• The height of the building is the side opposite the angle of elevation from the car to the girl.
• The distance of the car from the foot of the building is the side adjacent to this angle.
• The angle of depression from the girl to the car is 45°. Due to alternate interior angles, the angle of elevation from the car to the top of the building is also 45°.

• Height of the building (Opposite side) = 25 m
• Angle (θ) = 45°
• Distance of the car from the foot of the building (Adjacent side) = ?

The tangent function relates the opposite side, the adjacent side, and the angle:
tan(θ) = Opposite / Adjacent

tan(45°) = 25 m / Adjacent
We know that tan(45°) = 1.
1 = 25 m / Adjacent
Adjacent = 25 m / 1
Adjacent = 25 m

The distance of the car from the foot of the building is 25 m.