Question

I need help for the workings

Answer 1

The 2,500 m. distance and bearing of 110° of B from A and the location and 20 km/h motion of the drone gives;

(a) Height of the drone above B is approximately 669.9 meters

(b) The perimeter of ∆ABC is approximately 6,956.7 meters

(c) Angle of elevation of the drone from A when it is above C is approximately 11°

(d) The bearing of A from C is approximately 284.3°

Which trigonometric ratios can be used to find the bearing of point C?

The given parameters are;

Location of points A, B, C = Horizontal ground

Bearing of B from A = 110°

Length of AB = 2,500 m

Initial drone location = Vertically above B

Angle of elevation of drone from A = 15°

Drone's speed, v = 20 km/h

Time it takes the drone to be above C, t = 3 minutes

(a) The height of the drone above B is given by the trigonometric ratios for tangent, as follows;

$tan( \theta) = \frac{Opposite}{Adjacent}$

$Where \: \theta \: = Elevation \: angle$

Which gives;

$tan(15 ^ {\circ}) = \frac{Drone \: height}{2500}$

Drone height above B, h, is therefore;

h = tan(15°) × 2500 m. ≈ 669.9 m.

• The height of the drone above B, is approximately 669.9 m.

(b) Distance, d from B to C is found as follows;

d = v × t

Which gives;

d = 20 km/h × 3 minutes

Which gives;

d = (20,000/(60)) × 3 = 1,000

Therefore;

The distance from B to C is 1000 meters

The angle at B = 70° + 90° = 160°

According to the law of cosines, we have;

(AC)² = 2500²+1000²-2×2500×1000×cos(160°)

Which gives;

AC ≈ 3,456.7 meters

The perimeter, P, of ∆ABC is therefore;

P ≈ 2,500 + 1,000 + 3,456.7 ≈ 6,956.7

• The perimeter of ∆ABC is P ≈ 6,956.7 meters

(c) The angle of elevation of the drone from A is given by the equation;

Angle = arctan(h/(AC))

Which gives;

Angle = arctan(669.9/3456.7) ≈ 11°

• Angle of elevation of the drone at C from A is approximately 11°

(d) Angle C in ∆ABC is found using the law of sines as follows;

3,456.7/sin(160°) = 2500/sin(C)

Which gives;

C ≈ 14.3°

The bearing of A from C is therefore;

• Bearing = 270° + 14.3° = 284.3°

Learn more about the laws of cosines and sines here:

brainly.com/question/4372174

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