Answer th e foll owing que stions using what youve learned f

Answer th e foll owing que stions using what you\'ve learned from this unit. Write your responses in the space provided. 1. Find the length of a. (2 points) 15 12110

Solution

1) Applying cosine rule :a^2 = b^2 +c^2 -2bccosA

= 12^2 +15^2 -2*12*15cos110

= 492.127

a = 22.18

2) Applying cosine rule :a^2 = b^2 +c^2 -2bccosA

b = 18 ; c= 8 ; A = 43 deg

a^2 = 18^2 +8^2 -2*18*8cos43
   = 177.37

a = 13.32

3) Applying cosine rule :c^2 = a^2 +b^2 -2bccosA

a = 1/2 ;b= 1/3 ;C = 95 deg

c^2 = (1/2)^2 + (1/3)^2 -2(1/2)(1/3)cos95

= 1/4 +1/9 -1/3cos95

c= 0.62

Apply sine rule to dinf remaining angles:

a/sinA = c/sinC

sinA = a*sinC/c = 0.5*sin95/0.62

A = 53.45 deg

B = 180 -A -C = 31.55 deg

4) b = 32.6; c= 41.4 Angle A = pi/6

Applying cosine rule :a^2 = b^2 +c^2 -2bccosA

= 32.6^2 +41.4^2 -2*32.6*41.4 cospi/6

a = 20.95