Final answer:
The angle of elevation of the sun is approximately 34 degrees when a flagpole with a height of 24 feet casts a shadow of 36 feet.
Step-by-step explanation:
To find the angle of elevation of the sun when a flagpole 24 feet high casts a shadow 36 feet long, we will use trigonometry, specifically the tangent function which relates the angle of elevation with the opposite side (the height of the flagpole) and the adjacent side (the length of the shadow).
In this scenario, we can use the formula tangent(θ) = opposite/adjacent, which translates to tan(θ) = 24/36. By calculating the inverse tangent (arctan or tan-1) of this ratio, we obtain the angle of elevation:
θ = tan-1(24/36)
Calculate θ using a calculator and round to the nearest whole number:
θ ≈ tan-1(2/3)
θ ≈ 33.69°
Thus, the angle of elevation is approximately 34 degrees when rounded to the nearest whole number.