Maths Help (1 Viewer)

[Farhanthestudent005]

Determine all possible dimensions for triangle ABC given AB=6.2cm, angle ABC=35 degrees and AC=4.1

Give all dimensions correct to 1dp

Please help, it will be greatly appreciated. This is for my exam

Thanks

 

[imxprt]

So, you can find the answer by using the sin rule (or in combination with cosine rule too)

AB - 6.2 cm
BC - 7.1 cm
AC - 4.1 cm
∠ABC - 35°
∠BCA - 60°
∠CAB - 85°

 

[Eagle Mum]

The other possible triangle is with ∠BCA as an obtuse angle.
Since for any angle ‘a’ between 0 and 180 degrees, sin a = sin (180-a), the triangle with ∠BCA = 180-60 = 120 deg and ∠CAB = 25 deg, is the other solution.
x = 4.1 sin 25 / sin 35 = 3.0

 

[CM_Tutor]

This is definitely meant as a test to see if the answer recognises that the sine rule produces two potential answers. It can be that either is valid or that other information makes only one valid, but both must be considered.