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If the measure of angle A is 40* and the length of side b is 15 inches, which can be the length of side a if it is possible to form two triangles

Since we do not know where the angle of 23 degrees is located, then we can find the remaining side using the Pythagorean theorem. This can be done because we know that we have a triangle with a right angle.

We have then:
 27.6 ^ 2 + x ^ 2 = 30 ^ 2

From here, we clear the value of x.

We have then:

 x ^ 2 = 30 ^ 2 - 27.6 ^ 2x = sqrt{30 ^ 2 - 27.6 ^ 2}x = 11.8

Then, the area of the triangle is given by:

 A = (frac{1}{2}) * (b) * (h)

Where,

b: base of the triangle

h: height of the triangle

Substituting values:

 A = (frac{1}{2}) * (27.6) * (11.8)A = 162.8 ft ^ 2

Note: Maybe the height of the triangle is 27.6 instead of 11.8. This will depend on where the angle of 23.8 is located.

But for the moment of looking for the area of the triangle, this is not relevant because the product of the base for the height is the same.

Answer:

The approximate area of the triangle is:

 A = 162.8 ft ^ 2

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