Question

1. If a 650 cm ladder is placed against a building at a certain angle, it just reaches a point on the

building that is 520 cm above the ground. If the ladder is moved to reach a point 80 cm
higher up, how much closer will the foot of the ladder be to the building?
cm closer

Answer 1

The foot of the ladder will be 440 cm closer to the building.

Step-by-step explanation:

To find out how much closer the foot of the ladder will be to the building when it is moved 80 cm higher up, we can use the concept of similar triangles. First, we can calculate the angle at which the ladder is placed against the building using trigonometry.

sin(angle) = opposite/hypotenuse = 520 cm/650 cm = 0.8

angle = sin-1(0.8) ≈ 53.13°

Next, using the same angle, we can calculate the distance that the foot of the ladder will be closer to the building when it is moved up 80 cm:

new distance = 650 cm * sin(angle) - 80 cm = 520 cm - 80 cm = 440 cm

Therefore, the foot of the ladder will be 440 cm closer to the building.