Question

jerry (a cat) is looking at tom (a mouse) sitting on a table 41 feet away. if jerry could put a 57 foot board against the table, what angle of elevation would the board make with the floor?

Answer 1

Assuming that Jerry is at ground level and Tom is sitting on a table 41 feet away from Jerry, we can use trigonometry to find the angle of elevation that the board would make with the floor.

Let's call the height that the board reaches on the table "h". From the information given, we know that the distance from Jerry to the point where the board touches the table is 57 feet (the length of the board), and the distance from that point to Tom is 41 feet. We can set up a right triangle with these distances as the legs and "h" as the hypotenuse, as shown in the diagram below:

|\

| \

h| \ 41 ft

| \

|____\

57 ft

Using the Pythagorean theorem, we can find the value of "h":

h^2 = 57^2 + 41^2

h^2 = 3241 + 1681

h^2 = 4922

h = sqrt(4922)

h ≈ 70.1 ft

Now we can use trigonometry to find the angle of elevation of the board. We want to find the angle whose tangent is equal to the opposite side (h) divided by the adjacent side (57 ft):

tan(theta) = h / 57

theta = arctan(h / 57)

theta ≈ arctan(70.1 / 57)

theta ≈ 51.1 degrees

Therefore, the angle of elevation that the board would make with the floor is approximately 51.1 degrees.