An electric post is anchored to the ground by two guy wires attached on opposite sides. The guy wires make angles of 35• and 48• with the horizpntal that are 75 m apart. what is the length of each wire?
X=44.59
Y=55.79
To find the length of each guy wire, we can use trigonometry. Let's consider the two guy wires as two sides of a triangle, with the post as the third side.
First, let's label the given information:
- Angle A = 35 degrees
- Angle B = 48 degrees
- Distance between the guy wires (base) = 75 m
We can use the sine function to find the lengths of the guy wires. The sine function relates the opposite side of an angle to its hypotenuse.
Let's label the lengths of the guy wires as follows:
- Guy wire opposite angle A = a
- Guy wire opposite angle B = b
Using the sine function, we have:
sin(A) = a / 75
sin(35°) = a / 75
a = 75 * sin(35°)
sin(B) = b / 75
sin(48°) = b / 75
b = 75 * sin(48°)
Calculating the values of a and b:
a = 75 * sin(35°) ≈ 42.69 m (rounded to two decimal places)
b = 75 * sin(48°) ≈ 56.94 m (rounded to two decimal places)
Therefore, the length of each guy wire is approximately 42.69 meters and 56.94 meters, respectively.
To find the length of each guy wire, we can use trigonometry and the given angles and distance. Here's how to calculate it:
Step 1: Draw a diagram to visualize the problem. Label the electric post, the two guy wires, and the given angles and distance.
Step 2: Use the given information to identify the triangle formed by one of the guy wires, the horizontal line, and the ground. Let's choose the guy wire that makes an angle of 35° with the horizontal.
Step 3: Now, we can use the tangent function to find the length of the guy wire. The tangent of an angle is equal to the length of the opposite side divided by the length of the adjacent side.
In this case, the opposite side is the height of the electric post and the adjacent side is half of the distance between the guy wires since the guy wires are attached on opposite sides.
Let's represent the length of the guy wire as "x". Using the trigonometric definition:
tan(35°) = height of electric post / (half of the distance between guy wires)
tan(35°) = height of electric post / (75 m / 2)
Step 4: Simplify the equation and solve for the height of the electric post:
height of electric post = tan(35°) * (75 m / 2)
Step 5: Now that we have the height of the electric post, we can use the other guy wire's angle (48°) to find the length of the second guy wire. By using the same trigonometric equation as before, we can substitute the height of the electric post and solve for the length of the second guy wire.
length of second guy wire = tan(48°) * (75 m / 2)
Step 6: Plug in the values to calculate the length of each guy wire:
length of the first guy wire = tan(35°) * (75 m / 2)
length of the second guy wire = tan(48°) * (75 m / 2)
Calculate these expressions using a calculator to find the actual lengths of the guy wires.