Sam C.

asked • 03/04/22

Trigonometry Precalculus Triangle

Given a = 10 and B = 150° in triangle ABC, determine the values of b for which A has




(a) exactly one value


(b) two possible values


(c) no value.




Show your work.

Brenda D.

tutor
I agree with comment above. The student has stated that there is a Triangle ABC which would suggest there are angles A, B, and C with corresponding sides a, b, and c; if not then how do you have a triangle, how can any work be shown? Also there is no diagram the only information given is that a=10 and B=150 degrees. One might get the impression that B is the largest angle, therefore side b should be the longest side, since the angles in a triangle total 180 degrees, whatever A is, it must conform to 180-150 or being greater than 0 but less than 30 degrees. I think option c gets ruled out, but while other routes can be taken at least a diagram would help before any assumptions are made such as; is this an Isosceles Obtuse Triangle?
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03/05/22

Rodrigo F.

tutor
Law of sines gives us the relationship between sinA and b. Since 0<A<30, I'd answer only item a is possible.
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03/05/22

1 Expert Answer

By:

Raymond B. answered • 03/06/22

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a = 10


B = 150 degrees


values of b for which A have one, zero or more solutions?

sin150 =1/2


b>a as B>A


sinA/a = sin150/b


sinA/10 = (1/2)/b = 1/2b


sinA =10/2b = 5/b


bsinA= 5


b = 5/sinA


A<180-150 < 30


Let A = 15


then sinA= 0.25882


b= 5/0.25882 = 19.3185


C also = 15, and c also =10


b= 19.3185 has one solution for the triangle sides&angles


b <a, b<10, such as b=9 has zero solutions for the triangle


b > 19.3185 such as b = 20 has multiple solutions



b too small, and there's no solution, as b>a so b can't be <10


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