Given:
Hypotenuse = 2.1 ft
Height = 1.4 ft
To find:
The value of x.
Solution:
There is a right triangle in circle.
Let b be the base of the triangle.
Using Pythagoras theorem:
[tex]\text{Base }^{2}+\text{Height }^{2}=\text{Hypotenuse }^{2}[/tex]
[tex]b^2+(1.4)^2=(2.1)^2[/tex]
[tex]b^2+1.96=4.41[/tex]
Subtract 1.96 on both sides.
[tex]b^2+1.96-1.96=4.41-1.96[/tex]
[tex]b^2=2.45[/tex]
Taking square root on both sides.
b = 1.56
The line from the center of the circle bisect the chord.
So x = 2b
x = 2 × 1.56
x = 3.12
x = 3.1 (nearest tenth)
The value of x is 3.1 ft.