Final answer:
The measure of the angle formed by the short side and a diagonal of the rectangle is approximately 69 degrees.
Step-by-step explanation:
The question is asking for the measure, to the nearest degree, of the angle formed by the short side and a diagonal of a rectangle with sides 30 cm and 12 cm. We can use trigonometric functions to solve this problem. We will use the tangent function.
In a rectangle, the diagonal divides it into two right-angled triangles. We can identify the sides of this right-angled triangle as follows: the short side of the rectangle is the adjacent side, the long side is the opposite side, and the diagonal is the hypotenuse in relation to the angle we are looking for.
Tangent of an angle is the ratio of the opposite side to the adjacent side: tan(angle) = opposite/adjacent. By rearranging, we get angle = tan^-1(opposite/adjacent).
In this scenario, using the given lengths: angle = tan^-1(30 cm/ 12 cm). When we enter this expression into a calculator, we get an angle of about 68.2 degrees. The answer to the nearest degree is therefore 68 degrees, which isn't an option on the list. However, the closest option will be 69 degrees.
Learn more about Triangle Angles