Question

If an ant moves a distance x,then turn left 120 degree and travel x distance again and turn right 120 dgree and travel, he is 9 inches from the starting point, what is the value of x?

Answer 1

Answer:

X=4.5 inch

Explanation:

 look an equilatral triangle is formed hence all sides would be X so                                               one side+initial distance of X =9inch

X=4.5

Answer 2

Answer:

The value of  $x=\frac{9}{\sqrt{3} }$ .

Explanation:

• An equilateral triangle has all sides equal and all angles equal with value $60^{0}$.
• The sine of an angle is equal to perpendicular divided by the hypotenuse.

The formula for sine of an angle of the right-angled triangle:

Sin∠$X$=$\frac{Perpendicular}{Hypotenuse}$

Step 1:

The diagram is in the attachment:

When we look at the diagram ∠$ACB=60^{0}$.

We know that, $BC=AB$

So, ∠$BAC=$∠$BCA=60^{0}$

Hence, Δ$ABC$ is an equilateral triangle.

We also  observe that ∠$BCD=60^{0}$

As  ∠$BCD=$∠$ACB$

So, $AD$ is divided by $CB$ into two equal parts.

Step 2:

In right Δ$CED$

$sin60^{0} =\frac{\sqrt{3} }{2} =\frac{DE}{x}$

$\frac{\sqrt{3} }{2} =\frac{\frac{9}{2} }{x}$

$x=\frac{9}{\sqrt{3} }$

So, the value of  $x=\frac{9}{\sqrt{3} }$ .