An 8 foot long pole is propped against a fence to hold it up. The pole makes a 60 degree angle with the ground. How far above the ground does the pole come in contact with the fence?
sin 60 = h/8
so
h = 8 sin 60
by the way sin 60 = (1/2)sqrt 3
To find how far above the ground the pole comes in contact with the fence, we can use trigonometry. In this case, we can use the sine function since we are given the length of the hypotenuse (the 8-foot pole) and the measure of one of the acute angles (60 degrees).
We start by setting up a right triangle. The adjacent side represents the distance above the ground where the pole comes in contact with the fence, and the hypotenuse is the length of the pole (8 feet). The opposite side represents the distance from the top of the pole to the ground.
Next, we use the sine function:
sin(θ) = opposite/hypotenuse
sin(60 degrees) = opposite/8 feet
Rearranging the equation to solve for the opposite side:
opposite = sin(60 degrees) * 8 feet
Using a calculator, the sine of 60 degrees is approximately 0.866. Now we can calculate the distance above the ground where the pole comes in contact with the fence:
opposite = 0.866 * 8 feet
opposite ≈ 6.928 feet
Therefore, the pole comes in contact with the fence at a height of approximately 6.928 feet above the ground.