1 Solve each triangle ABC If the triangle is impossible show

1. Solve each triangle ABC. If the triangle is impossible, show why. If more than one triangle is possible, find all possible solutions. a) A-60.0°, b-30.0m, c-45.0m b) A 61.70, a = 789yd, b = 864yd c) a-4in, b-10in, c-5in

Solution

a) A = 60 degrees

b = 30 m

c = 45 m

applying law of cosines

a^2 = 30^2 + 45^2 - 2(30)(45) cos 60

a = 39.69 m

applying law of sines

a / sin A = b / sin B

39.69 / sin 60 = 30 / sin B

B = 40.89 degrees

C = 180 - ( 40.89 + 60)

C = 79.10 degrees

b)

A = 61.7 degrees , a = 78.9 yd , b = 86.4 yd

there are 2 solutions

78.9 / sin 61.7 = 86.4 / sin B

B1 = 74.62 degrees

B2 = 180 - (74.62) = 105.38 degrees

C1 = 43.68 degrees

C2 = 12.92 degrees

78.9 / sin 61.7 = c / 43.68

c1 = 61.89 yd

c2 = 20.03 yd

solutions are

traingle 1 :

angle A = 61.7 deg

B = 74.62 deg

C = 43.68 deg

a = 78.9 yd

b = 86.4 yd

c = 61.89 yd

triangle 2

angle A = 61.7 deg

B = 105.38 deg

C = 12.92 deg

a = 78.9 yd

b = 86.4 yd

c = 20.03 yd

c)

a = 4in , b = 10in , c = 5in

since a < b

so no triangles can be formed

one side is too long to form a closed regular triangle