Solved: The diagram below shows a helicopter hovering at point H, 380 m vertically above... [IB Mathematics Applications & Interpretation (AI)]

Solved: The diagram below shows a helicopter hovering at point H, 380 m vertically above... [IB Mathematics Applications & Interpretation (AI)] | RevisionDojo

The diagram below shows a helicopter hovering at point H, 380 m vertically above a lake. Point A is the point on the surface of the lake, directly below the helicopter. Minta is swimming at a constant speed in the direction of point A. Minta observes the helicopter from point C as she looks upward at an angle of 25°. After 15 minutes, Minta is at point B and she observes the same helicopter at an angle of 40°.

Write down the size of the angle of depression from H to C.

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Question

SLPaper 1

Write down the size of the angle of depression from H to C.

[1]

Verified

Solution

Angle of depression $= 25^{\circ}$ A1

1 mark total

Find the distance from A to C.

[2]

Verified

Solution

Identify correct trigonometric ratio: $\tan 25^{\circ} = \frac{380}{AC}$ M1
Rearrange to solve for AC: $AC = \frac{380}{\tan 25^{\circ}}$
Calculate result: $AC = 814.91...$
$AC = 815$ m (3 s.f.) A1

2 marks total

Find the distance from B to C.

[3]

Verified

Solution

Identify correct trigonometric ratio for AB: $\tan 40^{\circ} = \frac{380}{AB}$ M1
Calculate AB: $AB = \frac{380}{\tan 40^{\circ}} = 452.86...$ m
Subtract AB from AC: $BC = AC - AB$ M1
$BC = 814.91... - 452.86...$
$BC = 362$ m (3 s.f.) A1

3 marks total

Find Minta's speed, in metres per hour.

[1]

Verified

Solution

Convert time to hours: 15 minutes = 0.25 hours
Use speed formula: $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$
Substitute values: $\text{Speed} = \frac{362.04...}{0.25}$
$\text{Speed} = 1450$ metres per hour (3 s.f.) A1

1 mark total

Mathematics Applications & Interpretation (AI) International Baccalaureate (IB) Practice Question: The diagram below shows a helicopter hovering at point H, 380 m vertically above a lake. Point A is the point on the sur...