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?
60°
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Let's label the angle formed between the top of the building and the shadow as "θ". We know that the opposite side to this angle is the length of the shadow, which is 13 feet, and the hypotenuse is the diagonal distance of 15 feet.
Using the inverse sine function, we can determine the value of θ:
sin(θ) = opposite/hypotenuse
sin(θ) = 13/15
Taking the inverse sine of both sides:
θ = sin^(-1)(13/15)
Using a calculator to evaluate this expression, we find that θ ≈ 54.99°.
Therefore, the approximate angle formed between the top of the building and the shadow is 55°.