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.

Let's solve this problem. Step 1: Understand the setup. 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°. Step 2: Identify knowns and unknown. Height of the building (Opposite side) = 25 m Angle (θ) = 45° Distance of the car from the foot of the building (Adjacent side) = ? Step 3: Choose the appropriate trigonometric ratio. The tangent function relates the opposite side, the adjacent side, and the angle: tan(θ) = Opposite / Adjacent Step 4: Substitute the values and solve for the unknown. tan(45°) = 25 m / Adjacent We know that tan(45°) = 1. 1 = 25 m / Adjacent Adjacent = 25 m / 1 Adjacent = 25 m Step 5: State the final answer. The distance of the car from the foot of the building is 25 m. Last free one today — make it count tomorrow, or type /upgrade for unlimited.