Q13 of 62 Page 186

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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