Trigonometry — Question 135

Original QCE Vault practice · 6 marks

Q135 · Practice questionTechnology-activeComplex unfamiliar6 marks

QUESTION 135 (6 marks)

Ground stations

A

and

B

are

100

m apart on an east–west line, with

B

due east of

A

. A drone

D

is observed from

A

on a bearing of

035^\circ

and from

B

on a bearing of

300^\circ

. The angle of elevation of the drone from

A

38^\circ

. Determine the height of the drone above the ground, to the nearest metre.

WORKED SOLUTION

6 marks

ANSWER

Approximately

39

Worked solution

In the horizontal triangle, the angle at

A

55^\circ

and the angle at

B

30^\circ

, so the third angle is

95^\circ

. By the sine rule, the horizontal distance

AD=100\sin30^\circ/\sin95^\circ\approx50.191

m. Therefore the height is

AD\tan38^\circ\approx39.214

Converts the bearings into the two horizontal triangle angles.

[2 marks]

Uses the sine rule to determine horizontal distance

AD

[2 marks]

Uses the angle of elevation to determine height.

[1 mark]

States the height to the requested accuracy.

[1 mark]

Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.

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