Missing Angle

Question

Find the missing angle of each triangle below. Estimate answer to one decimal place.

      B
        x
        x   x A=23
        x       x
        x          x
c=14 x             x C
        x          x
        x 0=?x
        x   x  B=22
        x
      A

Answer 1

Hi Rachel,

for finding all angles when you have the measure of sides you need to use low of cosine. 

CosA = ( b.b +c.c-a.a)/(2bc)

cos A =(  22.22+14.14-23.23)/(2.22.14)

CosA = (484+196-529)/(616)

cosA = 151/616

cosA = .2451

A =75.81degree

for finding other missing angle is enough you plug in the below formula 

CosB=(a.a+c.c-b.b)/(2a.c)

cosC =(a.a+b.b-c.c)/(2a.b)

be carefull, we show  the sides of triangles by lower case and angles by upper case

I hope it is useful,

Good luck

 

Answer 2

Okay, so here we will use the Law of Cosines: a² = b² + c² - 2*b*c*cosθ

 

Simply plug in your values as follows:

 

(23)² = (22)² + (14)² - 2*(22)*(14)cosθ

529 = 484 + 196 - 616*cosθ

529 = 680 - 616*cosθ

 

Then solve for θ:

 

-151 = -616*cosθ

cosθ = 151 / 616

θ = cos^-1(151 / 616)

θ = 1.3 radian