The value of x is 4/3
What are trigonometric relations?
Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangles be ΔRST and ΔQRT
Now , from the figure
∠S = 90° in the triangle ΔRST
And RS = 2/√3
∠T = 60° in the triangle ΔRST
Now ,
sin 60° = opposite / hypotenuse
= RS / RT
= ( 2/√3 ) / RT
We know , sin 60° = √3 / 2
Substituting the value of sin 60° in the equation , we get
√3 / 2 = ( 2 / √3 ) / RT
Multiply by RT on both sides , we get
RT x ( √3 / 2 ) = ( 2 / √3 )
Divide by ( √3 / 2 ) on both sides , we get
RT = ( 2 / √3 ) x ( 2 / √3 )
RT = 4 / 3
Therefore , the value of RT = 4/3
Now , from the figure
∠R = 90° in the triangle ΔQRT
and ∠T = 45° in the triangle ΔQRT
So ,
tan 45° = opposite / adjacent
We know tan 45° = 1
Substituting the value for tan 45° = 1 in the equation , we get
1 = opposite / adjacent
1 = x / RT
Multiply by RT on both sides , we get
x = RT
So , x = 4/3
Hence , The value of x is 4/3
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. The requested probability is 0.40