Question

part v. finding mis
1.
14
15
x
3.
9
17
x

Explanation:

Step1: Apply Pythagorean theorem for the first triangle

For a right - triangle, by the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\). Let the two legs of the right - triangle be \(l_1\) and \(l_2\), and the hypotenuse be \(h\). First, find the length of the unknown side (let's call it \(y\)) of the right - triangle with hypotenuse \(15\) and one leg \(14\).

$$y=\sqrt{15^{2}-14^{2}}=\sqrt{(15 + 14)(15 - 14)}=\sqrt{29\times1}=\sqrt{29}$$

Then, for the second part (assuming the problem is to find \(x\) in the second right - triangle with hypotenuse \(17\) and one leg \(9\))

Step2: Apply Pythagorean theorem for the second triangle

Using the Pythagorean theorem \(x=\sqrt{17^{2}-9^{2}}\)

$$x=\sqrt{(17 + 9)(17 - 9)}=\sqrt{26\times8}=\sqrt{208}=\sqrt{16\times13}=4\sqrt{13}$$

Answer:

For the first - part (if it was a mis - labeled problem and we assume the first triangle's \(x\) was a wrong label and we focus on the second triangle), \(x = 4\sqrt{13}\approx14.42\)