Answer:
x = 28
Step-by-step explanation:
The tangent of a circle is always perpendicular (at a right angle) to the radius.
As the triangle ABC is a right triangle, we can use Pythagoras Theorem to find x.
Pythagoras Theorem
[tex]\sf a^2+b^2=c^2[/tex]
where:
- a and b are the legs of the right triangle
- c is the hypotenuse (longest side) of the right triangle
From inspection of the triangle ABC:
- a = BC = x
- b = AB = 96
- c = AC = 100
Substitute the values into the formula and solve for x:
[tex]\implies \sf x^2+96^2=100^2[/tex]
[tex]\implies \sf x^2=100^2-96^2[/tex]
[tex]\implies \sf x^2=784[/tex]
[tex]\implies \sf \sqrt{ x^2}=\sqrt{784}[/tex]
[tex]\implies \sf x=\pm28[/tex]
Therefore, as length is positive, the value of x is 28.
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