Solve each triangle. Round each measure to the nearest tenth of a unit.

Question

a)) In ∆ABC, ∠B=90 degrees, ∠C=47.1 degrees, c=9.7 cm

b)) In 𝐼𝑛 ∆𝐾𝐿𝑀,∠𝐾 = 90 degrees , 𝑚 = 12.4 𝑐𝑚 𝑎𝑛𝑑 𝑙 = 8.8𝑐m

Answer 1

B= 90, C=47.1 A= 90-47.1 = 42.9

c/sinC = 9.7/sin47.1 = b/sin90 = b/1 = b

b= 9.7./siin47.1 = 9.7/0.733 = 13.24 cm

a/sin42.9 = 13.24

a = 13.24sin42.9 = 9 cm

b^2 = a^2 + c^2

175 = 94 + 81

sides a,b and c are 9, 13.2 and 9.7

angles A,B and C are 42.9, 90 and 47.1 degrees

It's a right triangle so hypotenuse squared = sum of squares of the other 2 sides

k= sqr(12.4^2 + 8.8^2) = 15.2 cm

sinM/12.4 = sinK/k = 1/15.2

sinM = 12.4/15.2 =.816

M= 54.7 degrees

L = 90-54.7 = 35.3 degrees

K = 90 degrees

l = 8.8 cm, m =12.4 cm, k= 15.2 cm