Exercise 1 Page 495

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 = 35,

b = 12,

and

c = x .

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

x .

a^{2} + b^{2} = c^{2}

Substitute values

35^{2} + 12^{2} = x^{2}

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Solve for

x

Calculate power

1225 + 144 = x^{2}

Add terms

1369 = x^{2}

$LHS = RHS$

1369 = x

Rearrange equation

x = 1369

Calculate root

x = 37

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