Answer:
[tex]9\; \rm m[/tex].
Step-by-step explanation:
Assume that the run of this rafter is level. Then the height of the ridge (the line with a question mark next to it in the diagram) should be perpendicular to the line marked with [tex]\rm 12\; m[/tex]. The three labelled lines in this diagram will form a right triangle.
- The line marked as [tex]15\; \rm m[/tex] will be the hypotenuse of this right triangle.
- The line marked as [tex]12\; \rm m[/tex] will be one of the triangle's legs.
- The line representing the height of the ridge (the one with the question mark) will be the other leg of this right triangle.
Hence, the height of this ridge can be found with the Pythagorean Theorem. By the Pythagorean Theorem:
[tex](\text{First Leg})^2 + (\text{Second Leg})^2 = (\text{Hypotenuse})^2[/tex].
In this particular right triangle:
[tex](\text{Height})^2 + (12\; \rm m)^2 = (15\; \rm m)^2[/tex].
[tex](\text{Height})^2 = (15\; \rm m)^2 - (12\; \rm m)^2[/tex].
Therefore, the height of this ridge would be [tex]\sqrt{81}\; \rm m = 9\; \rm m[/tex]. (Note the unit.)
