Question

Find the length of OX

Answer 1

Answer:

Length OX = 7.09 units

Step-by-step explanation:

The diagram of the full question is attached to this solution.

Let the length of OX be x

Then length of OD = (13 - x)

From the image of the figure, it is given that

Angle BOL = Angle LOP

Let that angle be equal to θ

Angle BOL = Angle LOP = θ

But since lines BX, OL and PD are evidently parallel to one another, we can say that

Angle OPD = Angle LOP = θ (alternate angles are equal)

Also, Angle OBX = Angle BOL = θ (alternate angles are equal)

And from trigonometric relations,

Sin θ = (x/12)

And

Sin θ = (13 - x)/10

Since sin θ = sin θ

We can then equate

(x/12) = (13 - x)/10

cross multiplying

10x = 12 (13 - x)

10x = 156 - 12x

10x + 12x = 156

22x = 156

x = (156/22) = 7.091 = 7.09 to the nearest hundredth.

Hence, length OX = 7.09 units

Hope this Helps!!!