Paul is standing at the bottom of a hill that is 150 meters high. He measures the angle of the elevation of the top of the hill to be 32 degrees. If the slope of the hill is constant, how far will his walk to the top of the hill be
Sketch your right-angled triangle.
sin 32° = 150/x
x = 150/sin32
= ....
To find how far Paul's walk to the top of the hill will be, we can use the trigonometric function tangent (tan).
The tangent function relates the angle of elevation to the opposite and adjacent sides of a right triangle, where the angle is located. In this case, the opposite side is the height of the hill (150 meters) and the adjacent side is the distance Paul will walk.
We can use the formula: tan(angle) = opposite/adjacent.
Let's substitute the known values:
tan(32 degrees) = 150 meters/adjacent
To find the adjacent side (the distance Paul will walk), we rearrange the equation:
adjacent = 150 meters / tan(32 degrees)
Let's calculate it using a calculator or a programming language:
adjacent = 150 meters / tan(32 degrees)
adjacent ≈ 278.546 meters
Therefore, Paul will need to walk approximately 278.546 meters to reach the top of the hill.