Question

I am trying to find the circumference of an inscribed right triangle with legs 7 meters and 3 meters long. I missed the notes in class for this problem. I only know the definition of inscribed.

Answer 1

The drawing of a right triangle inscribed in a circle is shown below:

AD and BD are the legs of the triangle and AB is the hypotenuse, which coincides with the diameter of the circle centered at C.

The legs of the triangle measure 7 meters and 3 meters, so we can find the hypotenuse as follows:

$AB=\sqrt[]{7^2+3^2}$

We have applied the Pythagorean Theorem. Calculating:

$\begin{gathered} AB=\sqrt[]{49+9}=\sqrt[]{58} \\ AB\approx7.62m \end{gathered}$

The circumference of a circle is the diameter times pi:

$C=\pi d$

Substituting the value of AB (diameter):

$\begin{gathered} C=3.14\cdot7.62m \\ C\approx23.93m \end{gathered}$

Rounding to the nearest whole number, the circumference is 24 meters.