Question

Trig please help

Law of Sines and the Ambiguous Case.

In ∆ ABC, a =19, b = 15, and m < A = 50*
How many distinct triangles can be drawn given these measurements?

Answer 1

Answer:

  one triangle

Step-by-step explanation:

The given angle is opposite the longest given side, so this case is not ambiguous. These numbers define one triangle.

_____

Comment on ambiguity

The law of sines only gives rise to ambiguity (two solutions) only if the given angle is opposite the shorter of the two given sides, and the ratio of side lengths (short/long) is greater than the sine of the given angle.

In the extremely rare case of the side ratio being exactly equal to the sine of the angle opposite the shorter side, the triangle is a right triangle and there is exactly one solution.

Answer 2

Answer:

One

Step-by-step explanation:

19/sin(50) = 15/sinB

sinB = 0.6047719288

B = 37.2, 142.8

Since 142.8+50 = 192.8 > 180

It will not form a triangle.

So only one triangle possible with angle 37.2° at B