Answer:
[tex]x\approx 5.48[/tex]
Step-by-step explanation:
Draw a line from the center of the circle O to the end of either side of the line marked as 4. This line represents two things:
- A radius of the circle
- The hypotenuse of a right triangle with legs 5.1 and 2
In this case, both are important. Since [tex]x[/tex] is also a radius of the circle, the line must be equal to [tex]x[/tex], since all radii of a circle are equal. To find the length of this line, use the Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse of the triangle and [tex]a[/tex] and [tex]b[/tex] are the two legs of the triangle.
Since we're solving for the hypotenuse and the two legs are 5.1 and 2, we have:
[tex]5.1^2+2^2=c^2,\\26.01+4=c^2,\\c^2=30.01,\\c=5.47813836992\approx \boxed{5.48}[/tex] (round as necessary).
