### Instruction: What is the height of Jack's house, in feet, if the house casts a shadow 56 feet long at the same time a 21-foot tree casts a shadow that is 24 feet long? Express your answer to the nearest whole number.### Response: This problem involves similar triangles, since the sun's rays are parallel and form congruent angles with the ground and the objects.
Let x be the height of the house, then we have a proportion: x/56 = 21/24.
To solve for x, I can cross-multiply and get 24x = 56 * 21.
Simplifying, I get x = (56 * 21) / 24 = 49 feet.