Question

find the measure of $overline{bc}$. answer attempt 2 out of 2 submit answer

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula for finding side $BC$ (let $BC = a$, $AB = c = 15$, $AC = b = 16$) is $a^{2}=b^{2}+c^{2}-2bc\cos A$. Since no angle is given, if we assume this is a non - right triangle and no angle information, we cannot solve it with the given data. If we assume it is a right - triangle and $\angle A = 90^{\circ}$, then by the Pythagorean theorem $a=\sqrt{b^{2}+c^{2}}$.

Step2: Calculate using Pythagorean theorem

Substitute $b = 16$ and $c = 15$ into $a=\sqrt{b^{2}+c^{2}}$. So $a=\sqrt{16^{2}+15^{2}}=\sqrt{256 + 225}=\sqrt{481}\approx21.93$.

Answer:

$\sqrt{481}\approx21.93$