+0

# Trigonometry

0
64
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.

Guest Sep 25, 2017
Sort:

#1
+17616
+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

### 24 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details