I created a triangle using the polygon tool then increased the roundness in the toolbar options but instead of just rounding the tips like I thought it would it also bowed out the sides of the triangle (created curved sides instead of keeping them straight). Is there an option to keep the sides of the triangle in a straight line while just rounding the tips.

Like so?

Yes. That is exactly what I'm going for.

Don't know if it's a solution for you, it's just the first popped in my mind:
 

Faster:

-draw a triangle, straight sides;
-open Fill and stroke menu;

-adjust stroke thickness;

-set the round to "join";
-scale the triangle until you are satified about the radius of the rounded vertex

-disable "scale the radii of rounded corners" icon.

-modify the triangle as you wish, the radius of the corners doesn't change.

-to have a filled shape: convert stroke to path, then use Break Apart

Solution 2

-draw the polygon with the roundness you desire;
-adjust stroke width;

-convert stroke to path;

-Node tool: remove all the nodes that are useless in keeping the spikes rounded;

-select the segment to be straightened (one at once), use "make selected segments lines" button;

-use "break apart" to have a filled shape;

-the shape can be easily modified with dynamic or linked offset.

Fast faster furious:

Draw triangle with Polygon tool - convert Object to Path - then Path->Dynamic offset - adjust curvature - Object to path - done.

Faster than fast faster furious 😂: you can skip the conversion to path before offsetting.

Cool - Thanks to Inkscape's inconsistent behaviour. 👍