A guy wire is 11.2m long. It supports a vertical power pole. The wire is fastened to the ground 9.87m from the base of a 5.3m tall pole. Calculate the measure of the guy wire and the ground

we already know the wire is 11.2m long, so there's no need to calculate its measure.

what does the measure of the ground mean?

If the pole is 5.3m tall and the wire is attached 9.87m from the base and also at the top, it is in fact

√(9.87^2 + 5.3^2) = 11.2 meters long.

Looks like everything is given.

Ok thanks so much

To calculate the measure of the guy wire and the distance from the ground to the point where the wire is fastened, we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the guy wire is the hypotenuse, the base of the pole is one of the other sides, and the distance from the ground to the point where the wire is fastened is the remaining side.

Let's denote the length of the guy wire as c, the distance from the base of the pole to the point where the wire is fastened as a, and the height of the pole as b.

According to the Pythagorean theorem, we have the equation:

c^2 = a^2 + b^2

Substituting the given values, we have:

c^2 = (9.87m)^2 + (5.3m)^2

c^2 = 97.2369m^2 + 28.09m^2

c^2 = 125.3269m^2

Taking the square root of both sides, we find:

c ≈ √125.3269m^2

c ≈ 11.194m

Therefore, the measure of the guy wire is approximately 11.194 meters.

To find the distance from the ground to the point where the wire is fastened, we subtract the height of the pole from the length of the guy wire:

Ground distance = guy wire length - pole height

Ground distance ≈ 11.194m - 5.3m

Ground distance ≈ 5.894m

Therefore, the distance from the ground to the point where the wire is fastened is approximately 5.894 meters.