+0

# Trigonometry

0
303
1

(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.

Sep 25, 2017

#1
+17747
+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

Sep 25, 2017