Question

A cell tower, having a range of 10 miles, radiates signals in a circular path. A person is at (6, a), which is on the boundary position of the range of the tower. What is the value of 'a'?

• A. 8

Answer 1

The correct option is A 8

In the above figure, if point (x, y) lies on the circle, then using the Pythagoras theorem:

$x^2+y^2=r^2$

If the point (x, y) lies inside the circle, then:

$x^2+y^2<r^2$

If the point (x, y) lies outside the circle, then:

$x^2+y^2>r^2$

Now, point (6, a) lies on the boundary position of the circle.

$6^2+a^2={10}^2$

$\Rightarrow 36+a^2=100$

$\Rightarrow a^2=100-36$

$\Rightarrow a^2=64$

$\Rightarrow a=\sqrt{64}=8$

So the value of 'a' is 8.

The person is standing at (6, 8).