WMA11 Jan 2021

5. WMA11/01​​ Edexcel​​ IAL P1 January 2021 IAL Q5​​ (Radians: Radian Measure &​​ Trigonometry)

Figure 3 shows the plan view of a viewing platform at a tourist site.​​ 

The shape of the viewing platform​​ consists of a sector ABCOA of a circle, centre O, joined to a triangle AOD.​​ 

Given that​​ 

• OA = OC = 6m​​ 

• AD = 14m​​ 

• angle ADC = 0.43 radians​​ 

• angle AOD is an obtuse angle​​ 

• OCD is a straight line find​​ 

• the size of angle AOD, in radians, to 3 decimal places,​​ 

(3)

• the length of arc ABC, in metres, to one decimal place,​​ 

(2)

• the total area of the viewing platform, in m2​​ , to one decimal place.​​ 

(4)

SOLUTION

a-​​ 

Usimg sine rule to calculate angle x.​​ 

sin⁡x14=sin⁡0.436

sin⁡x=14sin⁡0.436

x=1.33658…. <π2∴angle

x=π-1.33650=1.80500…

∴AO^D=1.805 

b-​​ 

Length ABC is an arc length, which can be found by​​ using the formula of arc length.​​ 

l=rθ =62π-1.805=26.869…

l=26.9m

c-​​ 

Since viewing platform consist of a sector and a traingle, the total area of the viewing platform is​​ 

Total Area=Area of Sector+Area of Triangle

Therefore, the area fo a sector is​​ 

Area of sector =12r2θ

=12x 622π-1.805 

Whereas, the area of triangle is​​ 

Area of triangle=12absin⁡θ

=12x 6 x 14 xsin⁡0.90659

Hence,​​ 

Total Area=Area of Sector+Area of Triangle

=12x 622π-1.805+   12x 6 x 14 xsin⁡0.90659

Total Area=113.678

Total Area=113.7m2