A 9 meter ladder is one meter from the base of a building. How high up the building will the ladder reach?

The ladder would reach 8.9 meters up the building

Step-by-step explanation: Please refer to the attached diagram.

The ladder is placed on a wall, which is represented by line AB. It's distance from the base of the building is represented by line CB. To calculate how high up the ladder would reach on the building, we would need to calculate the value of line AC, which has been labelled as b.

What we have as shown in the diagram is a right angled triangle with the Hypotenuse given as 9 and one of the other two sides is given as 1.

We shall apply the Pythagoras theorem which states that

AB² = AC² + CB²

Where AB is the hypotenuse and AC and CB are the two other sides.

9² = b² + 1²

81 = b² + 1

Subtract 1 from both sides of the equation

80 = b²

Add the square root sign to both sides of the equation

√80 = b

8.9443 = b

Approximately, b = 8.9 meters

Therefore the ladder would reach up to 8.9 meters on the building