Question

11 *
34 yd
16 yd
b
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Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with hypotenuse $c$, and legs $a$ and $b$, the Pythagorean theorem is $a^{2}+b^{2}=c^{2}$. Here, $c = 34$ yd and $a = 16$ yd, and we want to find $b$. So, $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

Substitute $c = 34$ and $a = 16$ into the formula: $b=\sqrt{34^{2}-16^{2}}=\sqrt{(34 + 16)(34 - 16)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). Then $b=\sqrt{50\times18}=\sqrt{900}$.

Step3: Calculate the square root

$\sqrt{900}=30$ yd.

Answer:

30 yd