Review question

# Can we find the lengths and angles in this diagram of a roof? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6144

## Suggestion

In the diagram, which represents the roof of a house, $ABCD$ is a horizontal rectangle and $XY$ a line parallel to $AB$ and $DC$. $AB=40'$, $BC=XY=16'$ and $AX=BY=CY=DX=17'$. Calculate $(i)$ the height of $XY$ above the plane $ABCD$, …

Could we start by drawing a line perpendicular to $ABCD$ through either $X$ (or $Y$)?

How could we calculate its length? Maybe we could construct a triangle containing this side?

$(ii)$ the angle of inclination to the horizontal of the face $AXYB$, and $(iii)$ the angle of inclination to the horizontal of the edge $AX$.

Can we find more right-angled triangles which include one of these angles?