A building casts a shadow reaching 13 feet from the base of the building, with a diagonal distance of 15 feet from the top of the building. Using the inverse of sine, what is the approximate angle formed between the top of the building and the shadow?
Let's call the angle formed between the top of the building and the shadow angle B.
Using the inverse of sine, we can say that sin(B) = opposite/hypotenuse.
The opposite side is the height of the building and the hypotenuse is the diagonal distance from the top of the building to the base (which is 15 feet).
So, sin(B) = height/15.
We want to find angle B, so we use the inverse of sine:
B = sin^(-1)(height/15).
Since the shadow reaches 13 feet from the base of the building, the height of the building is the hypotenuse of a right triangle with a base of 13 feet. We can use the Pythagorean theorem to find the height:
height^2 + 13^2 = 15^2
height^2 + 169 = 225
height^2 = 225 - 169
height^2 = 56
height ≈ √56
height ≈ 7.48 feet
Now, we can substitute the height into the equation for angle B:
B = sin^(-1)(7.48/15)
Using a calculator, B ≈ 29.4 degrees.
Therefore, the approximate angle formed between the top of the building and the shadow is 29.4 degrees.