a radio cable has a support cable attached to its top. the support cable is 140 feet long and it is anchored in the ground 98 feet from the base of the radio tower. find the height of the radio tower (x), the angle of elevation (y), and the angle between the cable and the tower (z).

Answer 1

To find the height of the radio tower (x), we can use the Pythagorean theorem.

Let the height of the radio tower be x, the length of the support cable be 140 feet, and the distance from the base of the tower to where the support cable is anchored be 98 feet.

Using the Pythagorean theorem, we have:
x^2 + 98^2 = 140^2
x^2 + 9604 = 19600
x^2 = 9996
x = sqrt(9996)
x ≈ 99.98 feet

So, the height of the radio tower is approximately 99.98 feet.

To find the angle of elevation (y), we can use the inverse tangent function.

y = tan^(-1)(99.98/98)
y ≈ tan^(-1)(1.0204)
y ≈68.7 degrees

So, the angle of elevation is approximately 68.7 degrees.

To find the angle between the cable and the tower (z), we can use the inverse cosine function.

z = cos^(-1)(98/140)
z ≈ cos^(-1)(0.7)
z ≈ 45.57 degrees

So, the angle between the cable and the tower is approximately 45.57 degrees.