Using trigonometric relations we can write a system of equations, and solving that system we will get:
x = 3*√5
How to find the value of x?
We can view this as two right triangles, one smaller (in the right) and other larger, made of the two small triangles.
Also notice that the vertice in the right side is common for the two triangles, then we can use trigonometric relations that call for that angle.
If that angle is θ, we can see that x is the hypotenuse and 5 is the adjacent cathetus, then we can write:
cos( θ) = 5/x
For the larger triangle, the hypotenuse is 4 + 5 = 9, and the adjacent cathetus is x, then we can write:
cos(θ) = x/9
So we have the system of equations:
cos( θ) = 5/x
cos(θ) = x/9
Using substitution we can write:
5/x = x/9
If we multiply both sides by x we get:
5 = x^2/9
Now we can multiply both sides by 9 to get:
5*9 = x^2
√(5*9) = x^2
3√5 = x
That is the value expressed as a simplified radical.
Learn more about trigonometric relations:
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