Cotangent or cot(0) is the ratio of the adjacent side to the opposite side of a right triangle. Since the cosine of 0 is 1, we have:
cot(0) = Adjacent side / Opposite side
Let's assume the sides of the right triangle have lengths x and 24. Then, we have:
cot(0) = x / 24
Now, let's solve for x:
x / 24 = 7
x = 7 * 24
x = 168
Therefore, the length of the adjacent side of the right triangle is 168. We can now solve for the opposite side:
a / sin(a) = 168
a = 168
a = 45
This means the opposite side has length 45. Therefore, the triangle has dimensions 45, 168, and 24.
Now, we know the triangle is obtuse because the cosine of 0 is less than 0 and the tangent of 0 is negative. Therefore, the angle opposite the 168-side is larger than a right angle, but less than 180 degrees.