A 100 foot tall antenna sits part way up a hill. The hill makes an angle to 12 degrees with the horizontal. In other words, if you were going to walk up the hill, you would walk at an angle of 12 degrees. To keep the antenna stable, it must be anchored by 2 cables.The distance from the base of the antenna to the down point DOWN hill is 95 feet.Ignore the amount of cable needed to fasten the cable to the antenna or to the tie downs. How much cable is needed?
Please Draw and label if you can or give me the idea of this question.
Ok, on the down side cable. 100 distance up, 95 distance downhill, and the angle between those you can figure your self. YOu have SAS. Use the law of cosines to figure the cable length , you are given two sides, and included angle.
On the other cable, you present no info on how it is hooked up.
sorry, missed a sentence in the question:(
A 100 foot tall antenna sits part way up a hill. The hill makes an angle to 12 degrees with the horizontal.In other words, if you were going to walk up the hill, you would walk at an angle of 12 degrees. To keep the antenna stable,it must be anchored by 2 cables.The distance from the base of the antenna running to the tie down point on the cable UP hill is 85 feet.From the base of the antenna to the down point DOWN hill is 95 feet.Ignore the amount of cable needed to fasten the cable to the antenna or to the tie downs. How much cable is needed?
To better understand the question, let's draw a diagram.
First, draw a straight horizontal line to represent the ground. Label this line as "Horizontal."
Next, draw a slanted line to represent the hill. This line should make an angle of 12 degrees with the horizontal line. Label this line as "Hill."
From the base of the hill, draw another vertical line upwards to represent the antenna. Label this line as "Antenna."
At the highest point of the hill, draw a line downwards at a right angle to the horizontal line. Label this line as "Downhill."
The length of the horizontal line from the base of the antenna to the point where the vertical line and the downhill line meet should be labeled as 95 feet.
Now, we need to find the length of the cables needed to anchor the antenna. To do this, we can use trigonometry.
Since the hill makes an angle of 12 degrees with the horizontal, we can use the tangent function to find the length of the uphill cable.
The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the length of the hill, and the adjacent side is the horizontal distance from the base of the hill to the downhill point.
Let's denote the length of the uphill cable as "x."
Using the formula for the tangent, we can write:
tan(12) = hill length / 95
Solving for the hill length, we get:
hill length = 95 * tan(12)
Similarly, we can find the length of the downhill cable by using the same trigonometric approach.
Therefore, the total length of cable needed to anchor the antenna would be the sum of the uphill and downhill cables:
total cable length = uphill cable length + downhill cable length
total cable length = hill length + 95
Now, you can use the value of hill length calculated from the previous step to find the total cable length.