+0  
 
0
278
1
avatar

(a) In ΔABC, given that ∠ A = 38°, ∠ C = 85°, and c = 32 cm.

(b) In ΔABC, given that ∠ A = 24°, b = 12.5 m, and c = 13.2 m.

Guest Sep 25, 2017
 #1
avatar+17746 
+1

(a)  angle(A)  =  38o  and  angle(C)  =  85o   --->   angle(B)  =  180o - angle(A) - angle(B)  =  180o - 38o - 85o  =  57o

 

       Since you know side(c)  =  32 cm, you can use the Law of Sines to find sides a and b:

            side(a) / sin( angle(A) )  =   side(c) / sin( angle(C) )

            side(a) / sin( 38o )  =  32 / sin( 85o ) 

            side(a)  =  19.77 cm

 

            side(b) / sin( angle(B) )  =   side(c) / sin( angle(C) )

            side(b) / sin( 57o )  =  32 / sin( 85o ) 

            side(a)  =  26.94 cm

 

(b)  angle(A)  =  24o  and  side(b)  =  12.5 m  side(c)  =  13.2 m

 

      This describes a S-A-S situation, so you can use the Law of Cosines:

            a2  =  b2 + c2 - 2·b·c·cos(A)

            a2  =  (12.5)2 + (13.2)2 - 2·(12.5)·(13.2)·cos(24)

            a  =  5.39 m

 

       You can use the Law of Sines to find angle(B)

            [Warning:  Don't use the Law of Sines to find the largest angle in a triangle unless you have to!]

        sin(B) / side(b)  =  sin(A) / side(a)

        sin(B) / 12.5  =  sin(24o) / 5.39

        angle(B)  =  70.6o

 

        By subtracting angle(C)  =  180o - angle(A) - angle(B)  =  180o - 24o - 70.6o   =  85.4o

geno3141  Sep 25, 2017

7 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.