Question

How do you solve for the unknown lengths and angle measures of triangle ABC where angle C = 90 degrees, c = 10 and angle A = 30?

Answer 1

If `/_A = 30^@` and `/_C = 90^@`
then `/_B = 60^@` (since the interior angles of any triangle sum to `180^@`).

This is a standard right angled triangle whose sides are in the ratio:
`a:b:c = 1:sqrt(3):2`

That is for some constant `k`
`color(white)("XXXXX")` `(a,b,c) = (k*1, k*sqrt(3), k*2)`

We are told that `c= 10`
`color(white)("XXXXX")` `rarr k = 5`

Therefore
`color(white)("XXXXX")` `(a, b, c) = (5, 5sqrt(3), 10)`