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
45°
45°
90°
90°
60°
60°
30°
The inverse sine function gives us the angle when we know the opposite side and the hypotenuse of a right triangle. In this case, the opposite side is the height of the building (since the shadow is cast on the ground) and the hypotenuse is the diagonal distance from the top of the building to the end of the shadow.
Let's label the height of the building as "h" and the diagonal distance as "d".
We have the following information:
Opposite side = h = 13 feet
Hypotenuse = d = 15 feet
Using the definition of sine, we can set up the equation:
sin(angle) = opposite/hypotenuse
sin(angle) = h/d
sin(angle) = 13/15
To find the angle, we can take the inverse sine of both sides:
angle = sin^(-1)(13/15)
Using a calculator, the approximate angle is 53.13 degrees.
Therefore, the approximate angle formed between the top of the building and the shadow is 53.13°.