A television transmitter tower is 600 feet high. If the angle between the guy wire (attached at the top) and the tower is 57.8°, how long is the guy wire?

Q

To find the length of the guy wire, we can use trigonometry. Let's represent the length of the guy wire as "x".

Using trigonometry, the sine of the angle between the guy wire and the tower can be used to find the length of the guy wire. We can use the following equation:

sin(angle) = opposite/hypotenuse

In this case, the opposite side is the height of the tower (600 feet) and the hypotenuse is the length of the guy wire (x).

Therefore, we can write the equation as:

sin(57.8°) = 600/x

To find x, we can rearrange the equation as:

x = 600/sin(57.8°)

Now we need to calculate the value of sin(57.8°).

Using a calculator, sin(57.8°) is approximately 0.8415.

Now, substitute this value into the equation:

x = 600/0.8415

Calculating this, we find:

x ≈ 710.737 feet

Therefore, the length of the guy wire is approximately 710.737 feet.

To find the length of the guy wire, we can use trigonometry. Let's call the length of the guy wire "x".

We have a right triangle formed by the tower, the guy wire, and the ground. The height of the tower is the opposite side, and the length of the guy wire is the hypotenuse. The angle between the guy wire and the tower is given, so we can use the sine function.

The sine of an angle is equal to the ratio of the length of the opposite side to the length of the hypotenuse. In this case, the sine of 57.8° is equal to the height of the tower divided by the length of the guy wire:

sin(57.8°) = 600 / x

To solve for x, we can rearrange the equation:

x = 600 / sin(57.8°)

Using a scientific calculator or an online trigonometry calculator, we can evaluate this expression to find the length of the guy wire.

straight-forward trig ...

sin 57.8° = 600/length of wire
length of wire = 600/sin 57.8° ft
= ...