WMA11 Jan 2019

7. EDEXCEL IAL P1 new JAN 2019, Q7 (Trigonometry: Sine Rule)

Figure 3 shows the design for a structure used to support a roof.​​ 

The structure consists of four wooden beams, AB, BD,​​ BC and AD.​​ 

Given AB = 6.5m, BC = BD = 4.7m and angle BAC = 35°​​ 

(a) find, to one decimal place, the size of angle ACB,​​ 

(3)

SOLUTION

a- Using the sine rule to find the angle ACB.​​ 

sin⁡x6.5=sin⁡35 4.7

sin⁡x=6.5sin⁡354.7

x=52.489…, 127.51…

127.5o

(b) find, to the nearest metre, the total length of wood required to make this structure.​​ 

(3)

Total length=AB+BD+BC+AD

First, let us find the length AD. To find it, we will use sine rule.​​ 

ADsin⁡92.51=4.7sin⁡35o

AD=4.7sin⁡98.51sin⁡35=8.1863

Hence, the total length is

Total length=AB+BD+BC+AD

Total length=6.5+4.7+4.7+8.186

Total length=24.0863…

Total length=24m