Question

A 20-ft-long wire is used to support a television antaans. The wire is connected to the

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