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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