Trigonometry — Question 185

Original QCE Vault practice · 5 marks

Q185 · Practice questionTechnology-activeComplex unfamiliar5 marks

QUESTION 185 (5 marks)

Points

A

and

B

are

150

m apart, with

B

due north of

A

. A point

C

is observed on a bearing of

070^\circ

from

A

and a bearing of

120^\circ

from

B

, as shown. Determine

AC

and the perpendicular eastward distance of

C

from the line

AB

Survey diagram with A and B 150 metres apart north-south, and C located from bearings 070 degrees from A and 120 degrees from B.

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WORKED SOLUTION

Practice marking scheme

5 marks

ANSWER

AC\approx169.6

m and the perpendicular eastward distance is

\approx159.4

Worked solution

The angle at

A

70^\circ

. At

B

, the bearing of

BA

180^\circ

, so the interior angle is

60^\circ

. Hence angle

C=50^\circ

. By the sine rule,

AC/\sin60^\circ=150/\sin50^\circ

. The perpendicular eastward distance is

AC\sin70^\circ

Determines the interior angle at

A

[1 mark]

Determines the interior angle at

B

and hence angle

C

[1 mark]

Uses the sine rule correctly.

[1 mark]

Determines

AC

[1 mark]

Determines the perpendicular eastward distance.

[1 mark]

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

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Trigonometry — Question 185

QUESTION 185 (5 marks)

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