Question

Which equation can be used to find the measure of angle BAC?

tan−1(StartFraction 5 Over 12 EndFraction) = x
tan−1(StartFraction 12 Over 5 EndFraction) = x
cos−1(StartFraction 12 Over 13 EndFraction) = x
cos−1(StartFraction 13 Over 12 EndFraction) = x

Answer 1

Both tan−1(5/12) = x and cos−1(12/13) = x are correct.

Reason: In the 5–12–13 right triangle, for angle BAC the side opposite is 5, adjacent is 12 and hypotenuse is 13. So
- tan(BAC) = opposite/adjacent = 5/12 → BAC = tan−1(5/12),
- cos(BAC) = adjacent/hypotenuse = 12/13 → BAC = cos−1(12/13).

tan−1(12/5) and cos−1(13/12) are not valid for angle BAC (the last is impossible since 13/12 > 1).