Answer:
a. m∠T=82.2, m∠R=27.4, m∠M=70.4
Step-by-step explanation:
Let T, R and M represent the position of Trevor, Robert, and Maurice respectively,
Given,
TR = 13.5 feet,
RM = 14.2 feet,
TM = 6.6 feet,
Since, TRM forms a triangle, ( because sum of any two sides is greater than third side )
By the law of cosine,
[tex]TR^2=RM^2+TM^2-2\times RM\times TM\times cos M[/tex]
[tex]\implies cos M=\frac{RM^2+TM^2-TR^2}{2\times RM\times TM}[/tex]
By substituting the values,
[tex]cos M=\frac{14.2^2+6.6^2-13.5^2}{2\times 14.2\times 6.6}[/tex]
[tex]cos M=\frac{62.95}{187.44}[/tex]
[tex]\implies m\angle M=cos^{-1}(\frac{62.95}{187.44})=70.3763251924\approx 70.4^{\circ}[/tex]
Similarly,
[tex]cos R=\frac{TR^2+RM^2-TM^2}{2\times TR\times RM}[/tex]
[tex]=\frac{13.5^2+14.2^2-6.6^2}{2\times 13.5\times 14.2}[/tex]
[tex]=\frac{340.33}{383.4}[/tex]
[tex]\implies m\angle R=cos^{-1}(\frac{340.33}{383.4})=27.4189643117\approx 27.4^{\circ}[/tex]
[tex]cos T=\frac{TR^2+TM^2-RM^2}{2\times TR\times TM}[/tex]
[tex]=\frac{13.5^2+6.6^2-14.2^2}{2\times 13.5\times 6.6}[/tex]
[tex]=\frac{24.17}{178.2}[/tex]
[tex]\implies m\angle T=cos^{-1}(\frac{24.17}{178.2})=82.2047104959\approx 82.2^{\circ}[/tex]
Hence, option 'a' is correct.
