A right circular pole has a base radiur r and a vertical angle 2ydegrees.Find the height of the pole in terms of r and y
To find the height of the pole in terms of r and y, we can use the concept of trigonometry.
Let's consider the right triangle formed by the height of the pole, the radius of the base, and the hypotenuse of the triangle (which is the slant height of the pole).
In a right triangle, the sine function relates the opposite side to the hypotenuse. In this case, the opposite side is the height of the pole, and the hypotenuse is the slant height.
The formula for the sine of an angle is given by:
sin(angle) = opposite/hypotenuse
In our case, the angle is y, the opposite side is the height of the pole, and the hypotenuse is the radius of the base (r).
Therefore, we can write the equation as:
sin(y) = height of the pole / r
Solving for the height of the pole gives us:
height of the pole = r * sin(y)
So, the height of the pole in terms of r and y is equal to r multiplied by the sine of the vertical angle (2ydegrees).