Question

Question #8a4ec

Answer 1

It's impossible to answer this specifically without the diagram, but use the Law of Cosines.

Explanation:

If you have distances DP and DQ as well as the angle between them (or "Side-Angle-Side"), you can use the Law of Cosines to calculate the third distance.

The Law of Cosines states `c^2=a^2+b^2-2abcos(theta)` where `theta` is the angle between two sides with lengths `a` and `b` and `c` is the length of the third side.

In this case, we'd use `PQ^2=DP^2+DQ^2-2*DP*DQcos(theta)`.

Why do we use the Law of Cosines? It'd be nice if we could use the Pythagorean formula, `a^2+b^2=c^2`, to find the third side, but we know it only works for right triangles. The Law of Cosines looks pretty similar, though. The Pythagorean formula only works for right triangles because it's actually just a special case of the Law of Cosines. Check it out:

`c^2=a^2+b^2-2abcos(theta)`

If we use `theta = 90º`, `cos(theta) = cos(90º) = 0`.

`c^2=a^2+b^2-2ab*0`
`c^2=a^2+b^2-0`
`c^2=a^2+b^2`

The Law of Cosines is just a generalized version Pythagorean formula!