Ladder forms a right triangle with the wall and ground, measuring 10 meters long and 5 meters from the base to the wall.

We are given a right triangle formed by a ladder leaning against a wall.

- The ladder is the hypotenuse: 10 meters long.
- The distance from the base of the ladder to the wall is one leg: 5 meters.
- The height the ladder reaches on the wall is the other leg, labeled “h” — this is what we need to find.

This is a classic Pythagorean theorem problem.

The Pythagorean theorem says:

> In a right triangle,
> (leg₁)² + (leg₂)² = (hypotenuse)²

Let’s plug in the numbers:

One leg = 5 m
Other leg = h
Hypotenuse = 10 m

So:

5² + h² = 10²
→ 25 + h² = 100

Now subtract 25 from both sides:

h² = 75

Now take the square root of both sides:

h = √75

Simplify √75:

√75 = √(25 × 3) = √25 × √3 = 5√3

If we want a decimal approximation:

√3 ≈ 1.732
So 5 × 1.732 ≈ 8.66

But since the problem doesn’t specify, we can leave it as exact value or round appropriately. Looking at the diagram, it seems to expect a numerical answer — probably rounded to one or two decimals.

Let’s check our math again:

5² = 25
10² = 100
100 - 25 = 75 → correct
√75 ≈ 8.660 → so about 8.66 meters

In many school problems, they accept either exact form or decimal. Since the inputs are whole numbers and no instruction is given, let’s go with the simplified radical form unless told otherwise — but looking at context (ladder against wall), practical measurement suggests decimal.

Wait — let me double-check if I made any mistake.

Is the triangle really right-angled? Yes — the diagram shows a right angle symbol between the ground and the wall.

Are the labels correct? Ladder = 10m (hypotenuse), base = 5m, height = h — yes.

Calculation:

h = √(10² - 5²) = √(100 - 25) = √75 = 5√3 ≈ 8.66 m

I think that’s solid.

Final Answer:
8.66