If it is less than 1 there are two solutions and in very rare cases when it comes out exactly equal to 1 there is one solution and it is a right triangle.

Solution:

using sine rule $\frac{a}{sin(A)}=\frac{b}{sin(B)}$

given, a=20, b=15, A=40

so by using these values in the sine rule we get sin(B)=0.4820

so B<1 hence there will be two triangles in this case.

with one triangle with angle B=28.816 degrees

and other triangles with angles B=180-28.816 = 151.183 degrees.

If the given side opposite the given angle is longer than the other given side, there is always exactly one solution. In this problem, the given side b is opposite the given angle B and b is shorter than the other given side a so it is not immediately obvious. To find out, we use the law of sine. If the sine of the unknown angle for the given opposite side turns out to be greater than 1, there is no solution. If it is less than 1, there are two solutions, and in very rare cases, if it is exactly equal to 1, there is one solution which is a right triangle.

Learn more about Two triangles here:-brainly.com/question/21874653

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1 year ago