Expert: Vishwas K Hajirnis - 7/10/2004

Question
What is the formula for calculating two sides of a right angle triangle when length of base and angles are known

Answer
I assume the base is the hypotenuse.
Let ABC be the triangle with AC as the hypotenuse,
So m(<ABC)=90, and we need to know the lengths
of side AB and side BC.

sin(< BAC) = length BC / lenght AC
Therefore
lenght BC = length AC * sin(< BAC)  ...(1)
But length AC is given and angle BAC is also
known.
Similarly
sin(< BCA) = length AB / lenght AC
Therefore
lenght AB = length AC * sin(< BCA)  ...(2)
But length AC is given and angle BCA is also
known.

The values of sin(< BAC) abd sin(< BCA) can be
found by referring to mathematical tables or using
scientific calculator or using any spreadsheet
program like Excel / Lotus 1-2-3 etc.
Substituting these values in (1) and (2),
we get the lengths of sides other than the
hypotenuse.