Question

The height of a radio tower is 500 feet, and the ground on one side of the tower slopes upward at an angle of 10° (see the figure).

(a) How long should a guy wire be if it is to connect to the top of the tower and be secured at a point on the sloped side 100 feet from the base of the tower?

(b) How long should a second guy wire be if it is to connect to the middle of the tower and be secured at a point 100 feet from the base on the flat side?

Answer 1

Step 1 :

Pythagorean theorem :

In a right angular triangular hypotenuse is equal to the sum of the squares of the other two sides.

Step 2 :

(a)

The height of the radio tower is 500 ft.

Let the length of the guy wire is z.

Draw the diagram for the given data :

Observe the figure :

Solve for x  :

 

Solve for y  :

 

Solve for h  :

Step 3  :

From the Pythagorean theorem:

Substitute and in above equation.

The length of the guy wire is 492.6 ft.

Step 4  :

(b)

The guy wire is connected to middle of the tower.

Means that, ft.

Let the length of the guy wire is w.

Draw the diagram for the given data :

From the Pythagorean theorem:

The length of the second  guy wire is 269.3 ft.

Solution  :

(a) The length of the guy wire is 492.6 ft.

(b) The length of the second guy wire is 269.3 ft.