+0

# ​find angle c with trig

+2
192
2
+445

find angle c with trig

(there is an image so plz open and reply)

ZZZZZZ  May 17, 2017
edited by ZZZZZZ  May 17, 2017
Sort:

#1
+80866
+2

There are several approaches, but here's mine

Let's find  AD  using the Law of Sines

AD / sin ABD  = AB / sin BDA

AD /  sin(70)  =  75 / sin (90)

So....DC  =   90  - 75sin (70)

Similarly.... we can find BC  as  75 sin (20)

So......using the tangent

Tan ( C )   =    BC / DC

Tan (C)  =   [ (75) sin (20) /  (   90  - 75sin (70) ) ]

Using the arctangent

arctan   [ 75 sin (20) /  (   90  - 75sin (70) ) ]  = C  ≈  .92 rads  ≈  52.7°

CPhill  May 17, 2017
#2
+18827
+1

find angle c with trig

$$\begin{array}{|rcll|} \hline \tan(B) &=& \dfrac{c \cdot \sin(A)}{b-c\cdot \cos(A)} \quad & | \quad c = 75\ cm \quad b = 90\ cm \quad A = 20^{\circ} \\\\ \tan(B) &=& \dfrac{75 \cdot \sin(20^{\circ})}{90-75\cdot \cos(20^{\circ})} \\\\ \tan(B) &=& \dfrac{75 \cdot 0.34202014333}{90-75\cdot 0.93969262079} \\\\ \tan(B) &=& 1.31390875033 \\\\ B &=& \arctan(1.31390875033) \\\\ \mathbf{B} & \mathbf{=} & \mathbf{52.7256774464^{\circ}} \\ \hline \end{array}$$

heureka  May 17, 2017
edited by heureka  May 17, 2017
edited by heureka  May 17, 2017

### 21 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