Question

b. write your plan of attack and then solve.
step 1: ________
we know
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.
.
step 2: ________
we know
.
.
.
step 3: ________
we know
.
.
.

Explanation:

Step1: Identify the triangle type

This is a right - triangle. The Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) (where \(c\) is the hypotenuse) can be applied. Here, \(c = 13\) mm (hypotenuse), \(b=12\) mm (one of the legs), and \(a\) is the unknown leg.

Step2: Apply the Pythagorean theorem

Substitute the values into the formula \(a^{2}+12^{2}=13^{2}\).
So, \(a^{2}+144 = 169\).

Step3: Solve for \(a\)

Subtract 144 from both sides: \(a^{2}=169 - 144\).
\(a^{2}=25\).
Take the square root of both sides: \(a=\sqrt{25}\).

Answer:

\(a = 5\) mm