7.1 8 Find the area of the triangle if a=9inches, b=7inches, and α=34°. Round to the nearest tenth.

Question

Find the area of the triangle if a=9inches, b=7inches, and α=34°. Round to the nearest tenth.

Answer 1

use law of sines to find angle gamma. sin34/9 = sinB/7 = sin(gamma)/c =.56. 9sinB=7(.56) =sinB=3.91/9

= 0.434, B= 25.72 degrees, C= 180-25.72 - 34 = 180-59.72 = 120.28 degrees

use the law of cosines to find side c

c^2 = a^2 + b^2 -2abcos(gamma)

= 81 + 49 -2(9)(7)cos(120.28)

=130-126(-0.5)

=130 +63 = 193

c = sqr193) = 13.9

sides are 13.9, 7 and 9

Use Heron's formula to find area

A=sqr[(p)(p-13.9)(p-7)(p-9)] where p = half the perimeter = (13.9+7+9)/2 = 29.9/2 = 14.9

=sqr(1)(7.9)(5.9)(14.9) = sqr(694.5) = 26.4 square inches