Chapter 10 - NCPN
Chapter 10 - NCPN
Chapter 10 - NCPN
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Ongoing Assessment<br />
In PQR, m∠P = 35°, m∠R = 78°, and PQ = 9.5 in. Find the length of PR<br />
to the nearest tenth. 8.9 in.<br />
Finding Angle Measures Using the Law of Sines<br />
The Law of Sines can also be used to find missing angle measures in<br />
right triangles and non-right triangles. Sufficient information must be<br />
provided about the triangle so that a proportion with only one variable can<br />
be formulated.<br />
Example 2<br />
Finding the Angle Measure of a Triangle<br />
In RST, m∠R = 62°, RS = 14 meters, and ST = 16 meters. Find m∠T to<br />
the nearest tenth.<br />
Solution<br />
Draw and label LMN.<br />
Use the Law of Sines to solve for m∠T.<br />
sin<br />
−1<br />
sin 62° sin x°<br />
=<br />
16 14<br />
14sin<br />
62°<br />
= sin x°<br />
16<br />
⎛14sin<br />
62°<br />
⎞ −1<br />
⎜<br />
sin<br />
⎝ 16 ⎟ = (sin x°<br />
)<br />
⎠<br />
50.<br />
6°≈x<br />
The measure of ∠T is approximately 50.6°.<br />
Ongoing Assessment<br />
In MNO, m∠M = 83°, MN = 8 in., and NO = <strong>10</strong> in. Find m∠O to the<br />
nearest tenth. 52.6°<br />
Critical Thinking In Example 2, how could m∠S be found After finding<br />
m∠T, subtract m∠R and m∠T from 180° to find m∠S.<br />
<strong>10</strong>.5 The Law of Sines and Law of Cosines 463
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