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sweet [91]
3 years ago
10

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.

Mathematics
1 answer:
ki77a [65]3 years ago
7 0

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°.

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