WMA11 June 2022

• WMA11/01​​ Edexcel​​ IAL P1 June 2022, Q3 (Trignometry)

In the triangle ABC,​​ 

• AB = 21 cm​​ 

• BC = 13 cm​​ 

• angle BAC = 25°​​ 

• angle ACB = x°​​ 

• Use the sine rule to find the value of sinx°,​​ giving your answer to 4 decimal places.​​ 

(2)​​ 

Given also that AB is the longest side of the triangle,​​ 

• find the value of x, giving your answer to 2 decimal places.​​ 

(3)

SOLUTION

a- Using sine rule to find the value of sin x.​​ 

Let’s sketch the traingle and lable each side and angle as per the given data in the question.​​ 

sin⁡x21=sin⁡25o13

sin⁡xo=21sin⁡2513

sin⁡xo=21sin⁡2513

sin⁡xo=0.682691

sin⁡xo=0.6827

b-​​ 

sin⁡xo=0.682691

sin⁡xo= 0.6827

xo=sin-1⁡0.6827….

x=43.054o

Always remember, the sine rule sometime produces two possible solutions for a missing angle.​​ 

sin⁡θ=sin⁡(180-θ)

Since question emphsizes that the side AB is the largest side of the triangle, the angle opposite to AB side will also be greatest of all angles of a traingle, therefore, we need to find out the 2nd​​ possible angle produced by sine rule.​​ 

x=180-43.054

=136.9457o

x=136.95o