Triangle ABC is given where m < A = 33, a=15 in and the height h is 9 in. How many distinct triangles can be made with the given measurements
There are infinitely many triangles that can be formed with the given measurements, as long as the side lengths satisfy the triangle inequality theorem.
The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
In this case, side a = 15 in and height h = 9 in. Since we know angle A = 33 degrees, we can use trigonometry to find the lengths of the other two sides (b and c).
sin(33 degrees) = h / b
b = h / sin(33 degrees) = 9 / sin(33 degrees)
cos(33 degrees) = h / c
c = h / cos(33 degrees) = 9 / cos(33 degrees)
Using these equations, we can find the possible lengths of sides b and c. As long as these lengths satisfy the triangle inequality theorem, there are infinitely many distinct triangles that can be formed with the given measurements.