Triangle: how to find other sides, given angles and one side

[sycho53]

If you know the angles of a triangle are 90 degrees, 11.25 degrees and 78.75 degrees and you know the side between the 90 and 11.25 angles is 38 inches how do you determine the length of the other two sides?

 

[soroban]

Re: Triangle

Hello, sycho53!

For this problem, you are expected to know some Trigonometry . . .

If you know the angles of a triangle are 90°, 11.25° and 78.75°,
and you know the side between the 90° and 11.25° angles is 38 inches.
How do you determine the length of the other two sides?

    A *
      *   *
      *78.73° *
      *           *
      *               *
      *                   *
      *               11.25°  *
    C * * * * * * * * * * * * * * * B
                   38

We have: \(\displaystyle \:\tan11.25^o \:=\:\frac{AC}{38}\;\;\Rightarrow\;\;AC\:=\:38\cdot\tan11.25^o \:\approx\:\fbox{7.56}\)

We have: \(\displaystyle \:\cos11.25^o \:=\:\frac{38}{AB}\;\;\Rightarrow\;\;AB \:=\:\frac{38}{\cos11.25^o} \:\approx\:\fbox{38.74}\)