A guy wire from the top of a telephone post touches the ground at a point 7 meters from the foot of the post. If the wire and the post make an angle of 56°40', find the length of the guy wire.
The wire and the post form a rt. triangle with the gnd.
L = Hyp. = Length of wire.
X = 7 m.
A = 56.67o
L = X/Cos A
Well, it seems like the telephone post just can't "wire-t" for attention, huh? Alright, let's calculate the length of that guy wire!
To do that, we can use a little trigonometry. The length of the guy wire is the hypotenuse of a right triangle, and we have the angle and one of the sides. So, we just need to use some trig functions to find the missing side!
The side adjacent to the angle is the distance from the foot of the post to the point where the wire touches the ground, which is 7 meters. The hypotenuse is the guy wire, let's call it "x".
Now, using the cosine function: cos(angle) = adjacent/hypotenuse
Plugging in the values we have: cos(56°40') = 7/x
To solve for x, we rearrange the equation: x = 7/cos(56°40')
Calculating the value: x ≈ 15.68 meters (approximately)
So, the length of the guy wire is approximately 15.68 meters. I hope the telephone post appreciates being all "wired up" now!
To find the length of the guy wire, we can use trigonometry.
Let's label the length of the guy wire as GW. We can use the sine function to find GW.
sin(angle) = opposite / hypotenuse
Since the angle given is between the guy wire and the ground, the opposite side is 7 meters (the distance from the foot to the point where the guy wire touches the ground).
sin(56°40') = 7 / GW
To find GW, we need to isolate it on one side of the equation:
GW * sin(56°40') = 7
Now, we can solve for GW:
GW = 7 / sin(56°40')
Using a calculator, we can evaluate sin(56°40') and solve for GW:
GW ≈ 7 / 0.8311
GW ≈ 8.42
Therefore, the length of the guy wire is approximately 8.42 meters.
To find the length of the guy wire, we can use trigonometry.
Let's call the length of the guy wire "x". In this case, we have a right triangle formed by the guy wire, the post, and the distance from the foot of the post to the point where the guy wire touches the ground.
The angle between the guy wire and the ground is given as 56°40'. This means that the angle between the guy wire and the post is the complement of this angle, which is 90° - 56°40' = 33°20'.
Now, we can use the trigonometric function tangent to solve for "x". The tangent of an angle is the opposite side divided by the adjacent side. In this case, the opposite side is the distance from the foot of the post to the point where the guy wire touches the ground, which is 7 meters, and the adjacent side is the length of the post, which we want to find.
So, using the tangent function:
tan(33°20') = opposite / adjacent
tan(33°20') = 7 / x
To solve for "x", we can rearrange the equation:
x = 7 / tan(33°20')
Now, we can calculate the value of "x" using a calculator:
x ≈ 7 / tan(33°20') ≈ 7 / 0.6494 ≈ 10.781 meters
Therefore, the length of the guy wire is approximately 10.781 meters.