a 20 meter long cable is used to support a telephone pole holding it perpendicular to the ground. If the cable forms a 60grados angle with the ground how long mhigh up the pole should the cable be attached?

10✅3

10√3

To find out how high up the pole the cable should be attached, we can use trigonometry.

We are given that the cable forms a 60-degree angle with the ground. Let's label the height we want to find as 'h.'

Using trigonometry, we can use the sine function to relate the angle and the sides of the triangle formed by the cable, the ground, and the pole.

The sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse (the cable in this case).

In this scenario, the side opposite the angle of 60 degrees is the height 'h' that we want to find, and the hypotenuse is the cable with a length of 20 meters.

So, we have the equation: sin(60 degrees) = h/20

Using the values sin(60 degrees) ≈ 0.86603, we can solve for 'h':

0.86603 = h/20

To isolate 'h,' we multiply both sides of the equation by 20:

h = 0.86603 * 20 ≈ 17.32 meters

Therefore, the cable should be attached approximately 17.32 meters high up on the pole to hold it perpendicular to the ground.

the cable is the hypotenuse of the right triangle formed by the cable, pole and ground.

(height of attachment) / (cable length) = sin(60º)

h / 20 m = √3 / 2