Answer:
i) Area = 25 m²
ii) slope of roof = 36.87°
Step-by-step explanation:
(i) Let the midpoint of AB = M
Find BC by using Pythagoras' Theorem: a² + b² = c²
(where a and b are the legs, and c is the hypotenuse of a right triangle)
Legs = MB and MC, hypotenuse = BC
⇒ 1.5² + 2² = BC²
⇒ 6.25 = BC²
⇒ BC = √(6.25) = 2.5
Area of a rectangle = width x length = BC x BE
⇒ area of BCFE = 2.5 x 5 = 12.5
⇒ area of ACFD = area of BCFE = 12.5
Therefore area covered by tiles = 12.5 + 12.5 = 25 m²
ii)
The angle of the slope of the roof will be angle ∠B of the right triangle ΔCMB.
Using sin(A)/a = sin(B)/b = sin(C)/c
sin(90)/2.5 = sin(B)/1.5
0.4 = sin(B)/1.5
0.6 = sin(B)
∠B = 36.87°
