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? the answer is not 51.06
Let's denote the height of the building as h, the length of the shadow as s, and the diagonal distance as d. We can create a right triangle where the base is the length of the shadow, the height is the height of the building, and the diagonal line is the diagonal distance.
By definition of sine, we have sin(angle) = opposite/hypotenuse. In this case, the opposite side is the height of the building, and the hypotenuse is the diagonal distance.
Sin(angle) = h/d
To find the angle, we can take the inverse sine of both sides:
angle = sin^(-1)(h/d)
Substituting the given values, we have:
angle = sin^(-1)(13/15)
Using a calculator, we find that sin^(-1)(13/15) is approximately 51.06 degrees.
Therefore, the approximate angle formed between the top of the building and the shadow is 51.06 degrees.