Question

Using the Ambiguous Law of Sines, solve the following triangle. You will have two solutions.
In Triangle ABC:
a=9
c=15
angleA=35˚

Please solve step by step?

Answer 1

"Ambiguous"?

law of sines; a/sinA = b/sinB = c/sinC

where a is the side opposite angle A etc.

Answer 2

2 solutions? Well the law of sines states, \[\huge\color{red}{ \frac{Sin(A)}{a}=\frac{Sin(B)}{b} =\frac{Sin(C)}{c} }\]

Perhaps the hyp doesn't have to be integer, and then side c can be either hyp or one of the legs. Only this way there are TWO solutions.

Answer 3

yes correct

Answer 4

i dont understand how there are 2

Answer 5

SO you would have to draw 2 shapes in this case.

See?

Answer 6

ohhh i understand

Answer 7

Yeah, the first one is 3-4-5 pythagorean triple dilated by the scale factor of 3.
and the second would give you the hyp which will be irrational.

I think you have to solve each of those shapes fully to get each answer.

Answer 8

i can't get the answer

Answer 9

That's what we have the Sin law for.
\[\huge\color{blue}{ \frac{Sin~A}{a} =\frac{Sin~B}{b} =\frac{Sin~C}{c} }\]

a sin of angle divided by the side it forms, EQUALS a sin of another angle divided by the side it forms. (IN SAME TRIANGLE)

Answer 10

For example, in the first shape, you want to find angle B.
you would use

a^2+b^2=c^2

to find b,
and then plug in b into
\[\frac{Sin~B}{b~~~~(which~~~you~~~found)} =\frac{Sin~35}{9} \]

plug in b and solve for angle B.

Can you solve for angle B now?

Answer 11

yes i can