Question

Your given side ab with a length of 6 centimeters and side bc with a length of 5 centimeters. The measure of amgel A is 30. How many triangles can you construct using these measurements?

Answer 1

2

Explanation:

The given angle is opposite the shortest of the given sides, and sin(A) < 5/6, so there are two possible solutions.

The law of sines tells you that angle C will satisfy ...

sin(C)/ab = sin(A)/bc

sin(C) = ab/bc·sin(A) = 6/5·1/2 = 3/5

The given angle is 30°, so the sum of remaining angles must be less than 150°. There are two possible angles less than 150° that have a sine of 3/5:

C₁ = arcsin(3/5) = 36.87°

C₂ = 180° -arcsin(3/5) = 143.13°

You can construct two triangles with the given measurements.

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See the attachments for drawings of them.