Question

How do you solve the right triangle given A=41degrees, a = 17, b=9?

Answer 1

`/_B=49^@; /_C = 90^@; c= sqrt(370)`

Explanation:

Since the triangle is a right triangle, one of it's angles is `90^@`

Since `/_A = 41^@ rarr /_A != 90^@`

The hypotenuse is opposite the `90^@` and the hypotenuse is longer than either of the other two sides.
Since `b < a`
`b` can not be the hypotenuse and `/_B != 90^@`

`.: /_C = 90^@`

Since the interior angles of a triangle must add up to `180^@`
and since `/_A=41^@` and `/_C=90^@`
`.: /_B = 49^@`

Since (based on the above analysis) `c` is the hypotenuse
the length `c` is given by the Pythagorean Theorem as
`color(white)("XXX")c= sqrt(17^2+9^2) = sqrt(370)`