How do you solve the right triangle given a = 12, c = 6, C = 25°?

1 Answer
Alan P.
Oct 23, 2015

If /_A is the right angle
color(white)("XXX")/_B=65^@ and b=6sqrt(3)
If /_B is the right angle
color(white)("XXX")/_A=65^@ and b=6sqrt(5)

Explanation:

The given information allows for two possible configurations (see image below).

Interior angles of a triangle sum to 180^@
and since we have a right angle (i.e. 90^@) and /_C = 25^@ the third angle must be 65^@#

The length of side b can be calculated using the Pythagorean Theorem, but its specific value depends upon whether b is the hypotenuse or an arm of the right angle.
enter image source here

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