solve this triangle A=48° a=28.4m b=32.5m?

gift_1234

5 years ago

using the sine rule
a÷sin A= b÷ sin B = c÷sin C
to get sin B
a÷sin A = b÷sin B
28.4÷sin 48 = 32.5÷ sin B
cross multiply
sin 48 × 32.5 = sin B x 28.4
0.7431 × 32.5 = sin B × 28.4
24.15075 = sin B × 28.4
sin B = 24.15075÷28.4
sin B = 0.8504
B = sin^-1 (0.8504)
B = 58
To find angle C
sum of angles in a triangle = 180
C=180-(48+58)
C= 74
To find side c
a÷sin A = c÷ sin C
28.4÷sin 48 = c÷sin 74
c=sin 74 × 28.4 ÷ sin 48
= 0.9613 × 28.4 ÷ sin 48
= 27.30092 ÷ 0.7431
= 36.7m