A building casts a shadow reaching 13 feet from the base of a building, with a diagonal distance of 15 feet from the top of the building. Using inverse sine, what is the approximate angle formed between the top of the building and the shadow?(1 point)
To find the angle formed between the top of the building and the shadow, we can use the inverse sine function.
Let's consider the right triangle formed by the building, its shadow, and the diagonal from the top of the building to the end of the shadow.
We know the opposite side of the angle we are looking for is 13 feet (the length of the shadow) and the hypotenuse is 15 feet (the diagonal distance). The angle we are looking for is the angle opposite to the shadow and adjacent to the building's height.
Using the sine function, we have:
sin(θ) = opposite / hypotenuse
sin(θ) = 13 / 15
To find the angle, we take the inverse sine of this ratio:
θ = sin^(-1)(13/15)
θ ≈ 54.5 degrees
Therefore, the approximate angle formed between the top of the building and the shadow is 54.5 degrees.
60 degrees
30 degrees
45 degrees
90 degrees
Let's reconsider the calculation:
sin(θ) = 13 / 15
θ = sin^(-1)(13/15)
θ ≈ 54.5 degrees
Therefore, the approximate angle formed between the top of the building and the shadow is 54.5 degrees.