Answer:
B. False
Step-by-step explanation:
We apply cosine law in the given triangle for measuring the value of [tex]\theta[/tex] and write.
[tex]a^{2} = b^{2} +c^{2} -2*b*c*cos\theta[/tex]
[tex]5.3^{2} = 7^{2} + 4^{2} - 2*7*4*cos\theta[/tex] ( We put the value of a,band c which shown in the figure )
[tex]28.09 =49 +16 - 56*cos\theta[/tex]
[tex]28.09 =65 -56*cos\theta[/tex]
[tex]28.09 - 65 = -56*cos\theta[/tex]
[tex]-36.91 =-56*cos\theta[/tex]
[tex]\frac{-36.91}{-56}=cos\theta[/tex]
[tex]cos\theta =\frac{36.91}{56}[/tex]
[tex]\theta=arccos\frac{36.91}{56}[/tex]
[tex]\theta =48.768[/tex] degree (Approximate value of angle calculated with the help of online calculator). Hence the given approximate value of [tex]\theta =22.5[/tex] degree is false.
