what is the length of $overline{bc}$?\n9 units\n11 units\n15 units\n16 units
what is the length of $overline{bc}$?\n9 units\n11 units\n15 units\n16 units
Answer
Explanation:
Step1: Apply Pythagorean theorem
In right - triangle ABC, if the hypotenuse is AB = 17 and one leg is AC = 8, according to the Pythagorean theorem (AB^{2}=AC^{2}+BC^{2}), then (BC=\sqrt{AB^{2}-AC^{2}}).
Step2: Substitute values
Substitute AB = 17 and AC = 8 into the formula: (BC=\sqrt{17^{2}-8^{2}}=\sqrt{(17 + 8)(17 - 8)}) (using the difference - of - squares formula (a^{2}-b^{2}=(a + b)(a - b))). First, calculate ((17 + 8)(17 - 8)=(25)\times(9)=225). Then (BC=\sqrt{225}=15).
Answer:
15 units