m∠R = 27.03°
Solution:
Given In ΔQRP, p = 28 km, q = 17 km, r = 15 km
To find the measure of angle R:
Law of cosine formula for ΔQRP:
[tex]r^{2}=p^{2}+q^{2}-2 pq \cos R[/tex]
Substitute the given values in the above formula.
[tex](15)^{2}=(28)^{2}+(17)^{2}-2 (28)(17) \cos R[/tex]
[tex]225=784+289-952 \cos R[/tex]
[tex]225=1073-952 \cos R[/tex]
Switch the given equation.
[tex]1073-952 \cos R=225[/tex]
Subtract 1073 from both side of the equation.
[tex]-952 \cos R=-848[/tex]
Divide by –952 on both sides.
[tex]$ \cos R=\frac{106}{119}[/tex]
[tex]$ R=\cos^{-1} \left(\frac{106}{119}\right)[/tex]
[tex]R=27.03^\circ[/tex]
Hence m∠R = 27.03°.
