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Solve completely (all missing sides and all missing angles) using trig ratios or laws. Round to the nearest tenth.

Solve completely (all missing sides and all missing angles) using trig ratios or laws-example-1
User Jayveesea
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1 Answer

5 votes

Answer:

Explanation:

3. Use Cosine law to find the length of the unknown side (PR)

q² = p² + r² - 2prCos Q

q is the opposite side of ∠Q;

p is the opposite side of ∠P; p = 33

r is the opposite sides of ∠R ; r = 67

q² = 33² + 67² - 2* 33*67 Cos 19°

= 1089 + 4489 - 4422 * 0.95

= 1089 + 4489 - 4200.9

= 1377.1

q = √1377.1

q = 37.1

PR = 37.1

To find the angle use law of sin


\sf (q)/(Sin \ Q) =(p)/(Sin \ P)\\\\\\(37.1)/(Sin \ 19)=(33)/(Sin \ P) \\\\\\(37.1)/(0.33)=(33)/(Sin \ P)\\\\\\37.1* Sin \ P = 33 *0.33\\\\Sin \ P =(33*0.33)/(37.1)

Sin P = 0.3


P = Sin^(-1) 0.3\\

P = 17.5°

∠R = 180 - (19 + 17.5)

= 143.5°

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