Exercise 18 Page 755

Let's start by paying close attention to the diagram. Since VU is tangent to the circle, the angle it makes with the radius at the point of tangency is a right angle. Therefore, the triangle formed is a right triangle.

We can see that the lengths of the legs are x and 7. The length of the hypotenuse is 11. If we substitute these values in the equation of the Pythagorean Theorem, we will be able to find the value of x. Let's do it!

a^2+b^2=c^2

SubstituteValues

Substitute values

x^2+ 7^2= 11^2

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Solve for x

CalcPow

Calculate power

x^2+49=121

SubEqn

LHS-49=RHS-49

x^2=72

SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt(x^2)=sqrt(72)

SqrtPowToNumber

sqrt(a^2)=a

x=sqrt(72)

UseCalc

Use a calculator

x=8.485281...

RoundDec

Round to 1 decimal place(s)

x ≈ 8.5

Note that, when solving the equation, we only kept the principal root. This is because x represents the length of a side, and therefore it cannot be negative.