Answer:
- a) 16.4 m, 101°
- b) 6.22 m, 51 m²
Step-by-step explanation:
Find the measure of angle Q:
- 50° + (180° - 130°) = 100°
a) Find PR using the law of cosines:
- PR = √(8² + 13² - 28*13*cos 100°) = 16.4 m (rounded)
Find ∠P using law of sines:
- 16.4/sin 100° = 13/ sin P
- m∠P = arcsin (13 sin 100° / 16.4) = 51° (rounded)
The bearing of R from P is:
b)
Find the measure of h, the distance from Q to PR:
- h/ PQ = sin P
- h = PQ sin P
- h = 8 sin 51° = 6.22 m
Find the area of ΔPQR:
- A = 1/2PR*h
- A = 1/2(16.4)(6.22) = 51 m²
