Question

A set of stairs is being built as shown. What is the height of the stair?

3 triangles form stairs. Each triangle has a side length of 9 inches and hypotenuse of 15 inches.




The stair is
inches high.

Answer 1

To find the height of the stair, we need to understand the dimensions of the triangles forming the stairs. Each triangle has a side length of 9 inches and a hypotenuse of 15 inches.

Let's denote the sides of the right triangle as follows:
- One leg (height) = \( h \)
- The other leg (base) = 9 inches
- Hypotenuse = 15 inches

Using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the two legs (a and b), we have:

\[
c^2 = a^2 + b^2
\]

In this triangle:
- \( c = 15 \) inches
- \( a = 9 \) inches
- \( b = h \) inches

Substituting the known values into the Pythagorean theorem, we get:

\[
15^2 = 9^2 + h^2
\]

Calculating the squares:

\[
225 = 81 + h^2
\]

Now, solve for \( h^2 \):

\[
h^2 = 225 - 81
\]
\[
h^2 = 144
\]

Taking the square root of both sides:

\[
h = \sqrt{144}
\]
\[
h = 12
\]

Therefore, the height of each set of stairs (triangle) is \( 12 \) inches.

If there are 3 triangles, the total height of the stairs would be:

\[
\text{Total height} = 3 \times 12 = 36 \text{ inches}
\]

Thus, the height of the stair is:

\[
\text{The stair is } 36 \text{ inches high.}
\]