Question

find the length of side a in the right triangle, if b = 9 and c = 15. (the triangle is not drawn to scale.)
(there is a right triangle image with hypotenuse c, leg b, and leg a, right - angled between a and b)
select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
a. using radicals, a is exactly \square. the a, up to three decimal places, is approximately \square.
b. the a, is exactly \square. no approximation is necessary

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), so \(a^{2}=c^{2}-b^{2}\).
Substitute \(b = 9\) and \(c = 15\) into the formula: \(a^{2}=15^{2}-9^{2}\).

Step2: Calculate \(a^{2}\)

$$
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$$

Step3: Solve for \(a\)

Take the square root of both sides. Since \(a>0\) (length of a side), \(a=\sqrt{144}=12\).

Answer:

B. The \(a\) is exactly \(12\). No approximation is necessary.