Final answer:
To determine the angle of elevation, we subtract the student's height from the building's height to find the height difference and then use the tangent function with this value over the distance from the building.
Step-by-step explanation:
To find the angle of elevation from the student's head to the top of a 170-foot tall building when the student is standing 15 feet away from the building's base, we can use the tangent function in trigonometry. The student's height is 6 feet, so we need to consider the height from the student's eyes to the top of the building, which is 170 - 6 = 164 feet. The tangent of the angle of elevation θ is the opposite side (the height difference) over the adjacent side (the distance from the building).
In mathematical terms: tan(θ) = opposite/adjacent which translates to tan(θ) = 164/15. To find θ, we use the inverse tangent function: θ = arctan(164/15). The student will need a calculator to find this angle, as θ = arctan(10.9333), which would give them the angle of elevation in degrees.