Jessica is making an entry table in woodshop. She designs the table so the back piece has an X formation between the two back legs. The height of the legs is 2.5 feet and the diagonal distance from the top of one leg to the bottom of the other is 5 feet. Using the inverse of cosine, what is the approximate angle formed where the X formation meets the top of the table? Round your answer to the nearest whole degree.(1 point)
To find the angle formed where the X formation meets the top of the table, we need to use the inverse cosine function. The cosine of an angle is equal to the adjacent side divided by the hypotenuse.
Let x be the angle we are trying to find. The adjacent side is 2.5 feet (height of the legs) and the hypotenuse is 5 feet (diagonal distance).
cos(x) = adjacent/hypotenuse
cos(x) = 2.5/5
cos(x) = 0.5
Now, we need to find the inverse cosine of 0.5 to find the angle x.
x = cos^(-1)(0.5)
x ≈ 60 degrees
Therefore, the approximate angle formed where the X formation meets the top of the table is 60 degrees.