Q. 135.0( 1 Vote )

A roof has a cross section as shown in the diagram,

(i) Identify the similar triangles

(ii) Find the height h of the roof.


Answer :

In ΔYZW


Let YZW = x


ZYW = 90-x ( It is a right-angled triangle)


XYW = x ( ZYX is 90)


YZW = XYW ----(1)


Similarly,


XYW = XZY ----(2)


Now,


In ΔYWZ and ΔXYZ


WXY = ZXY (common)


YWZ = XYZ (by (1))


ΔYWZ ΔXYZ ----(3)


Now,


In ΔXWY and ΔXYZ


YXW = ZXY (common)


XYW = XZY (by (2))


ΔXWY ΔXYZ ----(4)


ΔXWY ΔXYZ ΔYWZ (by (3) and (4))


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