Find a if b = 154 yd, c = 156 yd and ∠ α = 94 °.

Question

Find  if  yd,  yd and °.

a=

Answer 1

a = 222.99 yards or 223 yds.

Use the law of cosines

a^2 = b^2 + c^2 - 2bc(cosA)

a^2 = 154^2 + 156^2 - (2154)(155)cos94

a = sqr( 154^2 + 156^2 -(2) 24,024(-.067)

A=94, cos94 = -0.0698

a = sqr(23716+24336+2(1676))

= sqr(51404) = 226.7 yards

or you could use the law of sines, but it's more complicated

B+C = 180-94= 86

C= 86-B

use the law of sines

a = 156sin94/sinB = 155sin94/sin(86-B)

156/sinB = 155/sin(86-B)

sin(86-B) = sin86cosB-cos86sinB

solve for B, then C = 86, but it's easier to just use the law of cosines