# Can you solve a question that gives you two side lengths of a right angled triangle without Pythagorean Theorem?

Jul 10, 2018

Yes you may. Consider the following example.

Since this is a right triangle, we may use primary trig ratios.

Call the angle between side $x$ and $20$ angle B. Then

sinB = 14/20 -> B ~~44.427˚

We can also say that

$\tan B = \frac{14}{x}$

So divide 14 by the tangent of B.

$x = 14.28$

This is the same answer you would get via the pythagorean theorem.

$x = \sqrt{{20}^{2} - {14}^{2}} = 14.28$

Hopefully this helps!