Name: Ali
Who is asking: Other
Level of the question: Middle

Question: How can this be solved?

A 25 foot ladder is leaning against a building. The base of the ladder is 7 feet from the building. How high up the building does the ladder reach?


Hi Ali.

If you draw this, you will see a triangle formed by the building, the ground and the ladder. Assuming the ground is level and the building is straight upright (rather than, say, the leaning Tower of Pisa!), then the angle formed by the ground and the building is a right angle (90 degrees).

With triangles where one of the angles is 90 degrees (we call this a "right triangle") there is a famous equation called the Pythagorean Formula which says that if you know the length of two of the sides, you can calculate the third. The formula looks like this:

c2 = a2 + b2

The c represents the length of the side opposite the right angle so a and b are the "legs" of the triangle (the other two sides). In your problem, the ladder itself is the one opposite the right angle and since you know the distance on the ground, you know two out of three sides.

Now you can re-arrange the equation and solve for the height.

Hope this helps!
Stephen La Rocque>