17N.1.SL.TZ0.T_10

pestleMathematicsAISLPaper 117N· sl-3-2-2d-and-3d-trigsource ↗

Emily’s kite ABCD is hanging in a tree. The plane ABCDE is vertical.

Emily stands at point E at some distance from the tree, such that EAD is a straight line and angle BED = 7°. Emily knows BD = 1.2 metres and angle BDA = 53°, as shown in the diagram

N17/5/MATSD/SP1/ENG/TZ0/10

T is a point at the base of the tree. ET is a horizontal line. The angle of elevation of A from E is 41°.

Find the length of EB.

[3]

Write down the angle of elevation of B from E.

[1]

Find the vertical height of B above the ground.

[2]

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

Units are required in parts (a) and (c).

$\frac{{{\text{EB}}}}{{\sin 53{\rm{^\circ }}}} = \frac{{1.2}}{{\sin 7{\rm{^\circ }}}}$ (M1)(A1)

Note: Award (M1) for substitution into sine formula, (A1) for correct substitution.

$({\text{EB}} = ){\text{ }}7.86{\text{ m}}$ $\,\,\,$ OR $\,\,\,$ $786{\text{ cm }}(7.86385 \ldots {\text{ m}}$ $\,\,\,$ OR $\,\,\,$ $786.385 \ldots {\text{ cm}})$ (A1) (C3)

[3 marks]

34° (A1) (C1)

[1 mark]

Units are required in parts (a) and (c).

$\sin 34^\circ = \frac{{{\text{height}}}}{{7.86385 \ldots }}$ (M1)

Note: Award (M1) for correct substitution into a trigonometric ratio.

$({\text{height}} = ){\text{ }}4.40{\text{ m}}$ $\,\,\,$ OR $\,\,\,$ $440{\text{ cm }}(4.39741 \ldots {\text{ m}}$ $\,\,\,$ OR $\,\,\,$ $439.741 \ldots {\text{ cm}})$ (A1)(ft) (C2)

Note: Accept “BT” used for height. Follow through from parts (a) and (b). Use of 7.86 gives an answer of 4.39525….

[2 marks]

Examiners’ report

[N/A]