Final answer:
Using the tangent function of the given angle of elevation, the height of the Skylon Tower is approximately 274 m when rounded to the nearest meter.
Step-by-step explanation:
To find the height of the Skylon Tower, we can use trigonometry. Given that the angle of elevation to the top of the tower from a point 60 m away from its base is 78°, we can use the tangent function which relates the angle of elevation (θ) to the opposite side (height of the tower) and the adjacent side (distance from the base of the tower).
Tangent of an angle θ is given by: tan(θ) = opposite/adjacent. Here, θ = 78° and the adjacent side is 60 m. Plugging the values into the formula: tan(78°) = height / 60 m
To find the height, rearrange the formula: height = tan(78°) * 60 m. Now calculating the height using a calculator: height ≈ tan(78°) * 60 m ≈ 274.45 m (unrounded). To the nearest meter, the height is 274 m.