Question

Find AB, given that AC=16 and BC=6. Round answer to the nearest tenth.

Answer 1

AB = 14.8

Step-by-step explanation

An angle on the circumference subtended by the diameter is 90º. Therefore ABC is a right triangle, where the right angle is angle B. We have AC = 16 - this is the hypotenuse of the triangle - and BC = 6 - this is one of the sides. To find the other side, AB, we can use the Pythagorean theorem:

`\begin{gathered} AC^2=AB^2+BC^2^{} \\ 16^2=AB^2+6^2 \\ AB=\sqrt[]{16^2-6^2} \\ AB=\sqrt[]{256-36} \\ AB=\sqrt[]{220} \\ AB=2\sqrt[]{55}\approx14.8 \end{gathered}`