Question

A 30 -meter cable is attached to the top of an antenna tower to help keep it upright. the cable is tethered to the ground meters away from the base of the tower. a right triangle with base length 20 meters, height h, and hypotenuse 30 meters. an antenna sits at the top of the triangle where the height and hypotenuse meet. what is the height of the antenna tower? round the answer to the nearest tenth of a meter. meters

Answer 1

To find the height of the antenna tower, we can use the Pythagorean theorem. By substituting the values into the equation and solving for the height, we get approximately 22.4 meters.

Step-by-step explanation:

To find the height of the antenna tower, let's use the Pythagorean theorem. In the given triangle, the base is 20 meters, the hypotenuse is 30 meters, and the height is unknown.

According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore, we have:

20² + h² = 30²

Simplifying the equation, we can calculate the height:

400 + h² = 900

h² = 900 - 400

h² = 500

h = √(500)

h ≈ 22.4 meters

Answer 2

To find the height of the antenna tower, we use the Pythagorean theorem with the given hypotenuse of 30 meters and base of 20 meters. Upon calculation, the tower's height is found to be approximately 22.4 meters when rounded to the nearest tenth.

Step-by-step explanation:

The student is asking about the height of an antenna tower that forms a right triangle with a cable and the ground. We have two sides of the triangle: the hypotenuse (30 meters) and the base (20 meters). To find the height h, we can use the Pythagorean theorem which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

The formula looks like this: c² = a² + b²

Solving for the height h (which corresponds to a in our case):

• h² = c² - b²
• h² = 30² - 20²
• h² = 900 - 400
• h² = 500
• h = √500
• h ≈ 22.4

Therefore, the height of the antenna tower is approximately 22.4 meters, rounded to the nearest tenth of a meter.