You are skiing down a mountain with a vertical height of 1500 feet. The distance from the top of the mountain to the base is 3000 feet. What is the angle of elevation from the base to the top of the mountain?
To find the angle of elevation, we can use the trigonometric tangent function (tan). The angle of elevation is the angle between the horizontal line at the base of the mountain and the line of sight from the base to the top of the mountain.
We can set up a right triangle where the height of the mountain is the opposite side, and the distance from the base of the mountain to the top is the adjacent side. Let's call the angle of elevation "θ".
Using the tangent function, we have:
tan(θ) = opposite/adjacent
In this case, the opposite side is the height of the mountain (1500 feet) and the adjacent side is the distance from the base to the top of the mountain (3000 feet).
Plugging in these values, we have:
tan(θ) = 1500/3000
Now, we can solve for θ by taking the inverse tangent (arctan) of both sides:
θ = arctan(1500/3000)
Using a calculator or an online tool, you can find the inverse tangent of 1500/3000, which is approximately 26.6 degrees.
Therefore, the angle of elevation from the base to the top of the mountain is approximately 26.6 degrees.