Final answer:
To find the acute angle between the diagonals of a rectangle, we can consider the diagonals as vectors and use the dot product formula. Substituting the values a = 100 and b = 50, we can find the angle theta.
Step-by-step explanation:
To find the acute angle between the diagonals of a rectangle, we can consider the diagonals as vectors and use the dot product formula. Let's label the length of the rectangle as a and the width as b. The diagonal vectors will have magnitudes sqrt(a^2 + b^2) and will be at right angles to each other. Using the dot product formula, we can calculate the angle theta between the diagonals as:
cos(theta) = (a · b) / (|a| * |b|)
Substituting the values a = 100 and b = 50, we can find the angle theta.