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

Related questions
See all questions in The Law of Sines
Impact of this question
1857 views around the world
You can reuse this answer
Creative Commons License