Question

# Find the length of the third side of the right triangle, if one side = 4sqrt 3, and the hypotenuse = 8.

Non-right triangles and trigonometry

Find the length of the third side of the right triangle, if one side = $$\displaystyle{4}\sqrt{{3}}$$, and the hypotenuse = $$8$$.

$$\displaystyle{8}^{{2}}={b}^{{2}}+{\left({4}\sqrt{{3}}\right)}^{{2}}$$
$$\displaystyle{b}^{{2}}={8}^{{2}}–{\left({4}\sqrt{{3}}\right)}^{{2}}=$$
$$\displaystyle={64}–{48}={16}$$
$$\displaystyle{b}^{{2}}={16}$$
$$\displaystyle{b}={4}$$