Find a x b if a=5, b=10, and the angle between a and b is pi/4 radians.

Answer 1

SAS = 5-45-10

solve the triangle knowing 2 sides and the angle between them

use Laws of Sines and Cosines

c^2 = a^2 +b^2 -2abCosC

re-lettering the sides slightly

A =45 degrees

B=26.68 degrees

C = 106.33 degrees

a= 7.37

b = 5

c = 10

Area = 17.68 = bxcsinA = 1/2 x 5x10xsin45 = 25(.707) = 17.68

perimeter = 22.37

or

construct a parallelogram with sides 5 and 10, angle between them pi/4= 45

longer diagonal is

d = square root of (5^2 +10^2 -5(10)(2)Cos 106.33)= (125 +25Cos106.33)^.5

shorter diagonal = a= 7.37