Question

In the following triangle, find the values of the angles B and B1, which are the best approximations to the solution to this ambiguous case.

Answer 1

I am so confused on how to even start here, please give me some pointers?

Answer 2

you can use the law of sines to find the value of B1

then B will be the supplementary angle

Answer 3

Yes I see that but I am slightly confused
here is what I have tried
sin45/8.2=B1/10
can i just multiply both sides by ten to get B1?

Answer 4

well almost

to find B1 use

\[\frac{\sin(45)}{8.2} = \frac{\sin(B1)}{10}\]

Your calculation well see B1 as an angle larger than 45

Answer 5

so then

\[\sin(B1) = \frac{10 \times \sin(45)}{8.2}\]

Answer 6

i hope that helps you

Answer 7

or you could say

\[B1 = \sin^{-1}(\frac{10 \times \sin(45)}{8.2})\]

Answer 8

okay and that will find both angles then.

Answer 9

whhy did you take inverse sin?

Answer 10

yes, but looking at the diagram you drew, I would Say B1 would be larger than 90.... and B is less than 90.

the calculation above will only give an angle less than 90.

Answer 11

Hmm so the angles are different? the diagram I drew is not to scale

Answer 12

if B1 is less than 90... then the triangle that has B as an interior angle isn't a triangle as it's an isosceles triangle.
and you can't have 2 angles larger than 90

Answer 13

Hmm well it does say that this is an ambiguous case

Answer 14

so the calculation above will give B and B1 will be the supplemetary.

Does my explanation make sense?