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

1 Answer
Dec 12, 2015

#/_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)#