Chapter 11.6, Problem 2P

To determine

To find: the height of the telephone phone.

Answer to Problem 2P

  $AB=16m$ .

Explanation of Solution

Given:

The length of guywire is $20m$ is attached to the top of the telephone tower.

And the guywire is reached a point on the ground is 12m base of the telephone tower.

Calculation:

According to the base, the guywire is reached a point on the ground is 12m base of the telephone tower and length of guywire is $20m$ is attached to the top of the telephone tower. Thus,

  

Here, from right triangle ABC, AC is the hypotenuse. Therefore,

By using Pythagoras theorem, $A{C}^2=A{B}^2+B{C}^2$

Thus,

  $\begin{array}{l}A{C}^2=A{B}^2+B{C}^2\\ {20}^2=A{B}^2+{12}^2\left\{\text{substitutes the given value}\right\}\\ 400=A{B}^2+144\{\because {20}^2=400,{12}^2=144\}\\ A{B}^2=400-144\left\{\text{simplify}\right\}\\ A{B}^2=256\left\{\text{subtract the both terms}\right\}\end{array}$

  $\begin{array}{l}\therefore AB=\sqrt{256}\left\{\text{taking square root on both the sides}\right\}\\ \Rightarrow AB=\sqrt{{16}^2}\{\text{simplify}}\\ AB=16\{\sqrt{a^2}=a\}\end{array}$

Hence, the height of the telephone phone is $AB=16m$ .