Answer:
∠Q = 35.5°
Step-by-step explanation:
We are given;
q = 6.5 inches
o = 8.6 inches
∠P = 55°
Let's first use cosine rule to find p.
p² = q² + o² - 2qo cos P
Plugging in the relevant values;
p² = 6.5² + 8.6² - (2 × 6.5 × 8.6 × cos 55)
p² = 42.25 + 73.96 - 32.0629
p² = 84.1471
p = √84.1471
p = 9.17 inches
Using sine rule, we can find ∠Q;
p/sin P = q/sin Q
sin Q = (q•sinP)/p
sin Q = (6.5 × sin 55)/9.17
sin Q = 0.5806
Q = sin^(-1) 0.5806
Q ≈ 35.5°
