a cable attach to the top of a tv antenna is 100 ft. if the cable is fasten to the ground 28 ft from the base of the antenna how tall is the antenna?
Use the Pythagorean theorem. Solve for b.
a^2 + b^2 = c^2
28^2 + b^2 = 100^2
To find the height of the antenna, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the cable forms the hypotenuse, the height of the antenna forms one of the shorter sides, and the distance from the base of the antenna to where the cable is fastened to the ground forms the other shorter side.
Let's label the height of the antenna as 'h' and the distance from the base of the antenna to the fastened point on the ground as 'd'. From the given information, we have the following values:
Length of the cable (hypotenuse) = 100 ft
Distance from the base to the fastened point on the ground (one shorter side) = 28 ft
Using the Pythagorean theorem, we can set up the equation:
h^2 + d^2 = 100^2
Substituting the values we have, we get:
h^2 + 28^2 = 100^2
Simplifying the equation:
h^2 + 784 = 10,000
Subtracting 784 from both sides:
h^2 = 10,000 - 784
h^2 = 9216
Taking the square root of both sides:
h = √9216
h ≈ 96 ft
Therefore, the height of the antenna is approximately 96 ft.