Question

Refer to triangle ABC, which is not necessarily a right triangle. Find two triangles for which A = 55°, a = 6.5 ft, and b = 7.9 ft. (Round your answers for the angles B, C, B', and c' to the nearest whole number. Round your answers for the sides c and c' to one decimal place.) First triangle (assume B S 90°): в в o C = ft Second triangle (assume B' > 90°): B' = O C' ft

Answer 1

Solha Griven that, A = 55', 936.567 ,b= 7.9 ft. For first triangle (BS90) Let A ABC b= 7.9 ft C SS B a= 6:54 C We know that, Sin A sin o = since ine sinss 6.5 SinB 7.9 Sin B= sinss x 7.9 SinB = 0.995584796 B = 84.6139 (approx) B = 85' (approx) So, LA + L Bt Lc = 180° 55 +85' + C = 180' LC-180- 140 LC = 40 SO sina asing a sin 40 Sinss' C = s.10054 lappeer) Silft (approx)

triangle, for Second We know that, for 'B's go Sin (180-) = sino sin (180~95) = sings' Het bo ie Bags' : B' = 95'] Also LAT LB + 20'= 180' 55'+95'+Ld= 180 20=180-150 Kc'= 30 Now, din A Sin c Sin 55' 6+5 Sin 30' c' c'- Sin 30' xos sinss ' = 3.9675 (approx) a. ' = 3.97 ft c'= 4.0 ft