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?(1 point) Responses 90° 90° 60° 60° 45° 45° 30°
The approximate angle formed between the top of the building and the shadow can be calculated using the inverse sine function.
First, we can calculate the height of the building using the Pythagorean theorem:
Height^2 + 13^2 = 15^2
Height^2 + 169 = 225
Height^2 = 225 - 169
Height^2 = 56
Height ≈ √56
Height ≈ 7.5 feet
Now, we can calculate the angle using the inverse sine function:
sin(angle) = opposite/hypotenuse
sin(angle) = 7.5/15
sin(angle) = 0.5
Therefore, the angle formed between the top of the building and the shadow is approximately 30°.
Therefore, the answer is 30°.