Question

A 20-ft-long wire is used to support a television antaans. The wire is connected to the
antenna 15 ft above the ground. How far away from the base of the tower will the other
end of the wire be located?

Answer 1

Answer:

The distance of base of wire to the base of tower is 13.27 ft

Step-by-step explanation:

Given as :

The measure of wire connected between base ad antenna top = 20 ft

The wire is connected to the  antenna on tower at height h = 15 ft above the ground

Let The distance of base of wire to the base of tower = x ft

Let the angle drawn on ground = Ф

Now, According to question

In figure AOB

Sin angle = $\dfrac{\textrm perpendicular}{\textrm hypotenuse}$

i.e SinФ = $\dfrac{\textrm AB}{\textrm BO}$

Or,  SinФ = $\dfrac{\textrm h}{\textrm 20}$

Or,  SinФ = $\dfrac{\textrm 15}{\textrm 20}$

Or, SinФ = $\dfrac{\textrm 3}{\textrm 4}$

or, Ф = $sin^{-1}(\frac{3}{4})$

∴ Ф = 48.5°

Now, Again from figure

Tan angle = $\dfrac{\textrm perpendicular}{\textrm base}$

i.e TanФ = $\dfrac{\textrm AB}{\textrm OA}$

Or, Tan 48.5° = $\dfrac{\textrm h}{\textrm x}$

Or, 1.13 = $\dfrac{\textrm 15}{\textrm x}$

∴ x = $\dfrac{\textrm 15}{\textrm 1.13}$

i.e x = 13.27 feet

So, The distance of base of wire to the base of tower = x = 13.27 ft

Hence, The distance of base of wire to the base of tower is 13.27 ft Answer

Answer 2

The distance from the base of the tower to the end of the wire is 13.23 ft

The situation form a right triangle

Right triangle

Right triangle has one of its angle as 90 degrees.

The length of the wire is the hypotenuse of the triangle formed.

The wire connection 15 ft above the ground is the opposite side of the triangle formed.

Therefore, the distance of the base of the tower to the end of the wire can be calculated as follows:

c² = a² + b²

20² - 15² = b²

400 - 225 = b²

b = √175

b = 13.2287565553

b = 13.23 ft

learn more on right triangle here: https://brainly.com/question/16270099