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.

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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