Question

ABC is a triangle for which < ABC = 90°, AB= 10cm and BC=15cm, Find Ac? how do I solve this?

Answer 1

The Pythagorean theorem states:

$c^2=a^2+b^2$

where a and b are the legs and c is the hypotenuse of a right triangle.

Applying this theorem to triangle ABC (see the above diagram):

$AC^2=AB^2+BC^2$

Substituting with AB = 10 cm, BC = 15 cm, and solving for AC:

$\begin{gathered} AC^2=10^2+15^2 \\ AC^2=100+225 \\ AC^2=325 \\ AC=\sqrt[]{325} \\ AC\approx18\operatorname{cm} \end{gathered}$