small ship is lost at sea. Based on sightings of the ship and radar reports, the coast guard determines that the ship must be within a triangular area as illustrated below. Find the area

Question

Triangle

sides= 35km, 29km, and 40km

Answer 1

Use Heron's Formula

Call the sides a, b, and c.

s = semiperimeter = (1/2)(perimeter) = 52

Area = √[s(s-a)(s-b)(s-c)] = √[52(17)(23)(12)] = 493.9 km²

Answer 2

b=35km

a=29km

c=40km

α=acos((b^2+c^2-a^2)/(2bc))=44.88º

a/sinα=b/sinβ=c/sinγ

29/sin44.88=41.09749......=35/sinβ=58.3878....º=β

44.88

+ =103.37

-180=76.73218....º=γ