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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!!!
