A scalene triangle has base of 5cm. The angle opposite to the base is 63°, and a second angle is 72°. Find the area of the traingle

Using the sine rule it's possible to find the length opposite to the 72° angle. Therefore: 5/(sin63)=x/(sin72) x=5sin(72)/sin(63)=5.34 At this point, the third angle is needed. Since a triangle has a total sum of the angles of 180°, the following calculation is done: alpha=180-(63+72)=45° The formula for the area of a triangle is: Area=0.5absinC The two sides known are 5 and 5.34, and therefore the angle that is needed is subsequently the last one that was calculated, i.e.: 45° Adding these numbers in will yield the final result: Area=0.5x5x5.34xsin(45)=9.35cm^2