Question

Determine the number of possible triangles, ABC, that can be formed given A = 30°, a = 7, and b = 18.

Answer 1

none

Explanation:

We are given a triangle ABC with ∠A = 30°, sides a = 4 and b = 10.

According to the 'Law of Sines- Ambiguous Case', we have,

If a < b×sinA, then no triangle is possible.

If a = b×sinA, only one triangle is possible

If a > b×sinA, two triangles are possible.

So, we have,

b×sinA = 10 × sin30 = 10 × 0.5 = 5.

Now, as

4 = a < bsinA = 5.

We get, according to the rule, no triangle is possible.