Question

A triangle has sides A, B, and C. Sides A and B are of lengths `9` and `17`, respectively, and the angle between A and B is `(pi)/2`. What is the length of side C?

Answer 1

`C = sqrt(370)` or `~~ 19.24`

Explanation:

When you have the lengths of two sides of a triangle and the angle between, then you can solve the missing side with the law of cosines.

We want side `C`, which can be solved by the Law of Cosines formula `C = sqrt(A^2 + B^2 - 2(A)(B)cosc`, where `cosc` is the angle opposite to side `C`.

Let's substitute in the values and solve:
`C = sqrt((9)^2 + (17)^2 - 2(9)(17)cos(pi/2)`

Now simplify:
`C = sqrt(81 + 289 - 306(0)`

`C = sqrt(370)`

You can leave it like that, but if you want the answer to be in decimal form, it is `~~19.24` (rounded to the nearest hundredth's place).

Hope this helps!