SOLUTION: 1. find the area of the portion of the semi circle shown in the figure which is outside of the inscribed triangle. the figure has a triangle scalene and AC= 16 and CB=10.

Algebra ->  Circles -> SOLUTION: 1. find the area of the portion of the semi circle shown in the figure which is outside of the inscribed triangle. the figure has a triangle scalene and AC= 16 and CB=10.      Log On


   

Question 827493: 1. find the area of the portion of the semi circle shown in the figure which is outside of the inscribed triangle. the figure has a triangle scalene and AC= 16 and CB=10.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!


An angle inscribed in a semicircle is always a right angle.
Therefore ΔABC is a right triangle, and we can take its two legs
as its base and height.

So the area of ΔABC = expr%281%2F2%29AC%2ACB = expr%281%2F2%29%2816%29%2810%29 = 80

Since ΔABR is a right triangle, we can find the hypotenuse AB using
the Pythagorean theorem:

ABē=ACē+CBē
ABē=16ē+10ē
ABē=256+100
ABē=356
 AB=sqrt%28356%29 = sqrt%284%2A89%29 = 2sqrt%2889%29

AB is the diameter of the semicircle.  Since the radius is
half the diameter, the radius is sqrt%2889%29.

Area of a whole circle is pi%2Ar%5E2 so 
Area of a semicircle = expr%281%2F2%29pi%2Ar%5E2

So the area of this semicircle is 

expr%281%2F2%29pi%2A%28sqrt%2889%29%29%5E2 = expr%281%2F2%29pi%2A89 = 139.8008731

So the area of the portion of the semicircle which is outside of the 
inscribed right triangle ΔABC is 

area of semicircle - area of triangle =

139.8008731 - 80 = 59.80087308

Edwin