find the area of triangle pqr if q=6, r=7, and angle p=50°. also find p

Answer 1

use the law of cosines to solve for p

p^2 = 6^2 + 7^2 - 2(6)(7)cos50

p^2 =36 +49 -54 = 31

p = sqr31 = 5.57

use Heron's formula, h=half the perimeter, h= (6+7+5.57)/2 = 9.28

Area = sqr(h)(h-7)(h-6)(h-p) = sqr(9.28)(3.28)(2.28)(3.71) = sqr257.47 = 16.05