Question

See image for question.

Please show workings and diagrams.​

Answer 1

a) 16.4 km

b) 79 deegres.

c.10 km

Explanation:

Find the m<B:

-m<B= 360 deegres -310 deegres) +50 deegres=100 deegres.

a)

Find AC using law of counsines:

-AC=( 8 to the second power + 13 to the second power - 28×13× cos 100 deegres.

16.4 km

Answer 2

• a) 16.4 km
• b) 79°
• c) 10 km

Explanation:

Find the m∠B:

• m∠B = (360° - 310°) + 50° = 100°

a)

Find AC using law of cosines:

• AC = √(8² + 13² - 28*13*cos 100°) = 16.4 km (rounded)

b)

Find m∠A using law of sines:

• 16.4/ sin 100 = 13 / sin A
• m∠A = arcsin (13 sin 100 deg / 16.4) = 51° (rounded)

The bearing of C from A:

• 180° - (50° + 51°) = 79°

c)

Let the required distance is x:

• x/ BC = sin 50°
• x = BC sin 50°
• x = 13 sin 50°
• x ≈ 10 km (rounded)