When working in sRGB colour space, there are two problems with this colour.
1) The given colour (Adobe RGB 117 208 237 or #75d0ed) is defined in terms of the Adobe RGB colour space.
If an ignorant browser directly uses this RGB value as sRGB value, the result would obviously be a completely wrong colour:
2) The given colour is outside of the sRGB gamut.
Therefore, the Adobe RGB value of the given colour value cannot be correctly converted to a corresponding sRGB value.
You may want to consider two solutions for these problems:
Various browsers support ICC profiles (ICC version 2 or even version 4).
You may work in Adobe RGB colour space and use the given colour if you embed the Adobe RGB (1998) ICC Profile.
For example, both of the following squares have the same RGB value 117 208 237; however, the first square has the Adobe RGB (1998) ICC Profile and the second square has the sRGB IEC61966-2.1 ICC Profile.
If both colours look identical, your browser does not support ICC profiles (like Internet Explorer 8). For further tests see Is your system ICC Version 4 ready?
You may convert the Adobe RGB values to sRGB values and then work in sRGB colour space. If you cannot correctly convert the Adobe RGB value to a corresponding sRGB value (as in the given example, since the colour is outside of the sRGB gamut), you may want to select the closest matching sRGB colour.
For example, the given Adobe RGB value 117 208 237 corresponds to the sRGB value −8.3 209.2 238.7, which is outside of the sRGB gamut. The sRGB value of the closest matching sRGB colour is 0 209 239.
Note: The actual appearance of these examples depends on the capability and calibration of your system.