Trigonometry — Question 47

Original QCE Vault practice · 5 marks

Q47 · Practice questionTechnology-activeComplex unfamiliar5 marks

QUESTION 47 (5 marks)

Surveyors measure a baseline

AB=75

m. A point

C

is observed such that

\angle CAB=52^\circ

and

\angle CBA=68^\circ

. Determine the perpendicular distance from

C

AB

, to the nearest metre.

WORKED SOLUTION

5 marks

ANSWER

63

Worked solution

The third angle is

C=60^\circ

. By the sine rule,

AC=75\sin68^\circ/\sin60^\circ\approx80.30

m. The perpendicular height is

h=AC\sin52^\circ\approx63.27

m, so the nearest metre is

63

Determines

\angle C=60^\circ

[1 mark]

Uses the sine rule to determine

AC

[1 mark]

Obtains

AC\approx80.30

[1 mark]

Uses

h=AC\sin52^\circ

[1 mark]

Determines the perpendicular distance as

63

m to the nearest metre.

[1 mark]

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

How many marks did you earn?

Compare your working with the guide above.