Question

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

Answer 1

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°