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.

$\cos R=\frac{106}{119}$

$R=\cos^{-1} \left(\frac{106}{119}\right)$

$R=27.03^\circ$

Hence m∠R = 27.03°.