A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 4, respectively. The angle between A and C is #(17pi)/24# and the angle between B and C is # (pi)24#. What is the area of the triangle?

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Answer 1 · 2018-07-16T10:58:15

#5\sqrt2\ \text{unit}^2#

We know that the sum of all interior angles of a triangle is always #\pi# then the angle between sides A & B is given as

#\pi-\text{angle between sides A & C}-\text{angle between sides B & C}#

#=\pi-{17\pi}/24-{\pi}/24#

#={6\pi}/24#

#=\pi/4#

hence, the area of given triangle having sides #A=5#, #B=4# & their included angle #\angle C=\pi/4# is given as follows

#1/2AB\sin\angle C#

#=1/2(5)(4)\sin(\pi/4)#

#=10\cdot 1/\sqrt2#

#=5\sqrt2\ \text{unit}^2#