Trigonometry — Question 97

Original QCE Vault practice · 6 marks

Q97 · Practice questionTechnology-activeComplex unfamiliar6 marks

QUESTION 97 (6 marks)

Points

A

and

B

are

80

m apart on an east–west line, with

B

due east of

A

. A tower

T

is observed from

A

on a bearing of

035^\circ

and from

B

on a bearing of

315^\circ

. Determine

AT

and the perpendicular distance from

T

to line

AB

, to the nearest metre.

Question linkSyllabus coverage

WORKED SOLUTION

Practice marking scheme

6 marks

ANSWER

AT\approx57

m; perpendicular distance

\approx47

Worked solution

Using east/north coordinates, the ray from

A

t(\sin35^\circ,\cos35^\circ)

and the ray from

B=(80,0)

(80,0)+s(\sin315^\circ,\cos315^\circ)

. Solving gives

t\approx57.44

. Thus

AT\approx57

m. The north coordinate is

57.44\cos35^\circ\approx47.05

m, so the perpendicular distance is about

47

Represents the two bearings correctly.

[1 mark]

Forms equations for the two sight lines.

[1 mark]

Solves for the distance parameter from

A

[1 mark]

Obtains

AT\approx57.44

[1 mark]

Determines the north/perpendicular component.

[1 mark]

Reports approximately

57

m and

47

[1 mark]

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

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Trigonometry — Question 97

QUESTION 97 (6 marks)

Practice marking scheme

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