In the triangle shown a = 5 in., b = 7 in., and gamma = 25 degree. Define a, b,
ID: 3644917 • Letter: I
Question
In the triangle shown a = 5 in., b = 7 in., and gamma = 25 degree. Define a, b, and gamma as variables, and then: Calculate the length of c by substituting the variables in the Law of Cosines. (Law of Cosines: c2 = a2 + b2 - 2ab cos gamma) Calculate the angles alpha and beta (in degrees) using the Law of Sines. Verify the Law of Tangents by substituting the results from part (b) into the right and left sides of the equation. (Law of Tangents: a - b/a + b = tan[1/2(alpha - beta)]/tan[1/2(alpha + beta)]Explanation / Answer
theta=58*pi/180; a=[25.5;14*tan(theta)/(2.1*2.1+11);6*5*4*3*2;2.7^4;0.0375;pi/5]; %calculation of c b=5*5+7*7-2*5*7*cos(25*pi/180); c=sqrt(b) %calcualation of angle alpha e=5*sin(25*pi/180)/c; alpha=(asin(e))*180/pi %calcualation of angle beta f=7*sin(25*pi/180)/c; beta=(asin(f))*180/pi %verification tangent law %calcuation of LHS lhs=(5-7)/(5+7) %calculation of RHS alpha1=alpha*pi/180; beta1=beta*pi/180; rhs=tan(.5*(alpha1-beta1))/tan(.5*(alpha1+beta1))