Question

the building code for a set of indoor stairs is that the height of each riser is 7.75 inches and the depth of the tread is 10 inches. what is the diagonal length of each step? round to the nearest hundredth.

Explanation:

Step1: Identify the right - angled triangle

Each step forms a right - angled triangle, where the height of the riser and the depth of the tread are the two legs of the right - angled triangle. Let $a = 7.75$ inches and $b = 10$ inches.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem for a right - angled triangle is $c=\sqrt{a^{2}+b^{2}}$, where $c$ is the hypotenuse (diagonal length of the step). Substitute $a = 7.75$ and $b = 10$ into the formula: $c=\sqrt{(7.75)^{2}+10^{2}}$.

Step3: Calculate the squares

First, calculate $(7.75)^{2}=60.0625$ and $10^{2}=100$. Then $a^{2}+b^{2}=60.0625 + 100=160.0625$.

Step4: Calculate the square root

$c=\sqrt{160.0625}\approx12.65$ inches.

Answer:

$12.65$ inches