Question

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Please show workings and diagrams.​

Answer 1

• a) 16.4 m, 101°
• b) 6.22 m, 51 m²

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:

• 50° + 51° = 101°

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