Use the theorem of Pythagoras to find the length of the distance marked d in the diagram below, the slant length of the roof - Leaving Cert Mathematics - Question 9(c) - 2022

According to the Pythagorean theorem, we can express the relationship between the sides of the triangle as:

$d^2 = (8.5)^2 + (7)^2$

Now calculating the squares:

• $(8.5)^2 = 72.25$
• $(7)^2 = 49$

Thus, we have:

$d^2 = 72.25 + 49$

This gives:

$d^2 = 121.25$

Taking the square root to find d:

$d = ext{sqrt}(121.25) \approx 11.0 \, m$

Thus, the slant length of the roof, d, is approximately 11.0 m when rounded to one decimal place.