Question

given △bat, find the length of $overline{at}$.

Explanation:

Step1: Identify right - triangle and apply Pythagorean theorem

In right - triangle $\triangle BAT$ with $\angle A = 90^{\circ}$, by the Pythagorean theorem $BT^{2}=AB^{2}+AT^{2}$. We know $BT = 17$ cm and $AB = 15$ cm. So, $AT^{2}=BT^{2}-AB^{2}$.

Step2: Substitute values and calculate

$AT^{2}=17^{2}-15^{2}=(17 + 15)(17 - 15)$ (using the difference - of - squares formula $a^{2}-b^{2}=(a + b)(a - b)$). Then $AT^{2}=(32)\times(2)=64$.

Step3: Find the value of $AT$

Taking the square root of both sides, since $AT>0$ (as it represents a length), $AT=\sqrt{64}=8$ cm.

Answer:

$8$ cm