Question

Determine the number of possible triangles, ABC that can be formed given angle A=30 degrees, a=4 and b=6

Answer 1

B=60 and C=90. I hope this helps

Answer 2

One possible triangle

Explanation:

Given that in a triangleABC given one angle A =30 , two sides a and b

We can use sine angle formula for triangles

`(a)/(sinA) =(b)/(sinB) =(c)/(sinC)`

Substitute to get

`(4)/(sin30) =(6)/(sin B) =(c)/(sinC)`

`sin B = 0.75\\B=48.6`

C=
`180-30-48.6\\= 101.4`

`c=8sin 101.4\\c=7.842`

There can be only one triangle