Question

the question is in the picture below, if you could show all your work so i can see how to do it, that would be appreciated.

Answer 1

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:

`r^(2)=p^(2)+q^(2)-2 pq \cos R`

Substitute the given values in the above formula.

`(15)^(2)=(28)^(2)+(17)^(2)-2 (28)(17) \cos R`

`225=784+289-952 \cos R`

`225=1073-952 \cos R`

Switch the given equation.

`1073-952 \cos R=225`

Subtract 1073 from both side of the equation.

`-952 \cos R=-848`

Divide by –952 on both sides.

`$ \cos R=(106)/(119)`

`$ R=\cos^(-1) \left((106)/(119)\right)`

`R=27.03^\circ`

Hence m∠R = 27.03°.