A wire is attached to the top of a flag pole. The wire meets the ground 4 meters from the flag pole. The wire makes a 45 degree angle with the flag pole. How tall is the flag pole?
h/4=tan45
solve for h
To find the height of the flag pole, we can use the concept of trigonometry. Let's break down the problem and understand it better.
The wire meets the ground 4 meters from the flag pole, forming a right triangle. One side of the triangle is the height of the flag pole, the other side is the horizontal distance from the flag pole to where the wire meets the ground (4 meters), and the hypotenuse is the length of the wire.
The angle between the flag pole and the wire is given as 45 degrees. This is an important piece of information that we will use to solve the problem.
We can use the trigonometric function called sine to solve this problem. The sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.
In this case, the height of the flag pole is the side opposite the 45-degree angle, and the hypotenuse is the length of the wire.
So, using the sine function: sin(45 degrees) = height of the flag pole / length of the wire
We know that sin(45 degrees) = √2 / 2.
Therefore, √2 / 2 = height of the flag pole / length of the wire.
We can rearrange this equation to solve for the height of the flag pole:
height of the flag pole = (length of the wire) * (√2 / 2).
Given that the wire meets the ground 4 meters from the flag pole, we can substitute this value into the equation:
height of the flag pole = 4 meters * (√2 / 2).
Now we can calculate the height of the flag pole:
height of the flag pole = 4 meters * (√2 / 2) ≈ 2.83 meters.
Therefore, the height of the flag pole is approximately 2.83 meters.