A 20 m vertical telephone pole is standing on a 15 degree slope. One guy wire is attached 30 m up the slope and another guy wire is attached 30 m down the slope. What is the length of the guy wire attached down the slope?
I don't understand the question or what the diagram should look like.
well, shoot. Look from the side.
Draw a sloping line representing the ground.
Place a vertical line on the slope somewhere. Label the top T and the bottom B. That is the pole. Label its length 20.
Mark two points on the slope, equal distances from the pole. Label those distances 30. Label the downhill mark D and the uphill mark U.
You want the distance TD.
The angle TBD is 90+15 = 105°
By the law of cosines, the distance TD is found from
TD^2 = 30^2 + 20^2 - 2*30*20 cos 105°
40.13
40.1
Well, if you're confused, just imagine the telephone pole as the ultimate daredevil, trying to balance on a slope. It's like trying to stand on a slippery banana peel, but way higher up!
So, we have a 20-meter pole standing on a 15-degree slope. Let's imagine the slope as a ramp going down at a 15-degree angle. Now, imagine the telephone pole defying gravity and staying upright.
One guy wire is attached 30 meters up the slope, and another is attached 30 meters down the slope. So, we have two support wires pulling against the pole's inclination to make sure it doesn't go rolling down the hill.
To find the length of the guy wire attached down the slope, we can think of it as forming a nice right-angled triangle with the slope. The height of the triangle is 20 meters because that's the height of the pole, and the distance from the pole to where the wire is attached is 30 meters.
Now, to calculate the length of the guy wire attached down the slope, we can use some good old Pythagorean theorem magic. You see, the Pythagorean theorem is like the magician of math, always finding a way to bring things together harmoniously. In this case:
Length of guy wire down the slope = √[(Height of pole)^2 + (Distance from pole to where wire is attached)^2]
Or, in our case:
Length of guy wire down the slope = √[(20 m)^2 + (30 m)^2]
Now, let me grab my handy-dandy calculator and do some calculating here... Whoop-dee-doo... Crunch, crunch, crunch...
Okay, according to my highly accurate calculations, the length of the guy wire attached down the slope is approximately 36.055 meters. Ta-da!
So, to sum it all up, the daredevil pole has a support wire attached 30 meters up the slope and another 36.055 meters down the slope. That's quite the balancing act, wouldn't you say?
Sure, let me explain the scenario and how to visualize it.
In this question, we have a vertical telephone pole that is standing on a 15-degree slope. A slope refers to a surface that is at an angle rather than being completely flat. So, in this case, the ground beneath the telephone pole is not level.
To help support the pole and prevent it from falling over, there are two guy wires attached to it. A guy wire is a tensioned cable used to stabilize and secure structures. One guy wire is attached 30 meters up the slope, and the other guy wire is attached 30 meters down the slope.
We are asked to find the length of the guy wire attached down the slope.
To visualize this, imagine a vertical pole on a slope with two wires connected to it. One wire goes up the slope at an angle, and the other wire goes down the slope at an angle.
Now, let's use this information to find the length of the guy wire attached down the slope.
We can use trigonometry to solve this problem. Specifically, we can use the sine function, as it relates the angle of elevation or depression to the opposite side length and the hypotenuse.
Let's consider the right triangle formed by the telephone pole, the guy wire attached down the slope, and the ground. The vertical length of the pole (opposite side) is given as 20 meters, and we need to find the length of the guy wire (hypotenuse).
To use the sine function, we can write the equation:
sin(15 degrees) = opposite/hypotenuse
Now, we can substitute the known values into this equation and solve for the hypotenuse:
sin(15 degrees) = 20/hypotenuse
To solve for the hypotenuse, we can rearrange the equation:
hypotenuse = 20 / sin(15 degrees)
Using a scientific calculator, we can find that sin(15 degrees) is approximately 0.2588. Plugging this value into the equation:
hypotenuse = 20 / 0.2588
Calculating this expression, we find that the length of the guy wire attached down the slope is approximately 77.20 meters.
Therefore, the length of the guy wire attached down the slope is about 77.20 meters.