SOLUTION: How can I solve this exercise? Suppose A=30∘ and b=10. Then there is one value of a that is less than b and for which there is a unique triangle with the data A, a, and b. That

Question 1137442: How can I solve this exercise?
Suppose A=30∘ and b=10. Then there is one value of a that is less than b and for which there is a unique triangle with the data A, a, and b. That value of a is?
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

Draw a sketch with the 30 degree angle A at the left, one ray of the angle horizontal, and ray b upwards to the right at a 30 degree angle.

If ABC is a right triangle, then a/b = sin(30) = 1/2, so a=5.

If a is less than 5, no triangle is formed, because a is not long enough to reach from C to ray AB.

If a is greater than 5, then two different triangles can be formed -- one with angle B acute and another with angle B obtuse.

So the only value of a less than b for which there is a unique triangle with measurements A, a, and b is a=5.
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