Exercise 8 Page 617

To find the missing side of the triangle, we will use the Pythagorean Theorem. a^2+b^2=c^2

In the formula, a and b are the legs and c is the hypotenuse of a right triangle. We are given a triangle with a=x, b=7 and c=19.

Let's substitute these values into the formula and solve for x.

a^2+b^2=c^2

Substitute values

x^2+ 7^2= 19^2

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Solve for x

Calculate power

x^2+49=361

LHS-49=RHS-49

x^2=312

sqrt(LHS)=sqrt(RHS)

x=sqrt(312)

Split into factors

x=sqrt(4* 78)

sqrt(a* b)=sqrt(a)*sqrt(b)

x=sqrt(4)sqrt(78)

Calculate root

x=2sqrt(78)

Since a negative side length does not make sense, we only need to consider positive solutions.