Homework SourseSubstitute ur thetaR rthetatheta into the Helmholtz Boundary
Substitute u(r, theta)=R (r)theta(theta) into the Helmholtz Boundary Value Problem v^2 u+ lambda^2 u=0 u(1, theta)=0 to get r^2 R^n+rR^1+(landa^2 r^2-n^2)R=0 r(1)=0 Theta\" + n^2theta=0Given: ABC and ACD are triangles with: m(ACB)=60^0, AC=6, BC=8, CD=5. Find the area of the triangle ABD. 
Solution
In Triangle ABC : AC = 6 and BC = 8 ; Angle(ACB) = 60 deg
In Triangle ACD : AC = 6 and CD = 5 ; Angle(ACD) = 120 deg
Area of Triangle ABC = (1/2)AC*BCsin(ACB) = (1/2)*8*5*sqrt3/2
= 10sqrt3
Area of Triangle ACD = (1/2)AC*CDsin(ACD) = (1/2)*6*5sin120 =7.5 sqrt3
So, Area of Triangle ABD = 10sqrt3 + 7.5sqrt3 = 17.5sqrt3 = 30.31 sq inches
