Question

16. The carpenter on the Curb Appeal home improvement program wants to change the roof of a garden shed to give it more... well... curb appeal. He designs the roof shown in the diagram below but then remembers that an apex angle greater than 70° requires additional truss structures for stability. These additional truss structures are expensive and the homeowner wants to avoid any unnecessary cost. Will the carpenter need to redesign the roof? Justify your answer with mathematical reasoning. [3 marks] Apex angle 8 feet 6% feet 70°

Answer 1

A 8.5ft 6.75ft 78 B A Apex Angle B=70° By lam of sines sin (C) - AB sin(B) sin (c) sin (70) 8.5 sin(C) = (675) x sin(70) 8.5 Ас. - 6.75 C = 46.26° A + B + C =180 At70+48.26=180 A = 61.749 As LA is less than 70, there is no need to redesign