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Date	May 2019	Marks available	3	Reference code	19M.1.SL.TZ2.T_9
Level	Standard Level	Paper	Paper 1 (with calculator from previous syllabus)	Time zone	Time zone 2
Command term	Find	Question number	T_9	Adapted from	N/A

Question

A ladder on a fire truck has its base at point B which is 4 metres above the ground. The ladder is extended and its other end rests on a vertical wall at point C, 16 metres above the ground. The horizontal distance between B and C is 9 metres.

Find the angle of elevation from B to C.

[3]

a.

A second truck arrives whose ladder, when fully extended, is 30 metres long. The base of this ladder is also 4 metres above the ground. For safety reasons, the maximum angle of elevation that the ladder can make is 70º.

Find the maximum height on the wall that can be reached by the ladder on the second truck.

[3]

b.

Markscheme

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

${\text{tan}}\,B = \frac{{12}}{9}$ (A1)(M1)

Note: Award (A1) for 12 seen, (M1) for correct substitution into tan (or equivalent). Accept equivalent methods, such as Pythagoras, to find BC and correct substitution into other trig ratios. If ${\text{ta}}{{\text{n}}^{ - 1}}\left( {\frac{{16}}{9}} \right)$ seen award (A0)(M1)(A0).

53.1° (53.1301…°) (A1) (C3)

Note: If radians are used the answer is 0.927295…; award at most (A1)(M1)(A0).

[3 marks]

a.

$30\,{\text{sin}}\,70^\circ + 4$ (M1)(M1)

Note: Award (M1) for ${\text{sin}}\,70^\circ = \frac{x}{{30}}$ (or equivalent) and (M1) for adding 4.

32.2 (32.1907…) (m) (A1) (C3)

Note: If radians are used the answer is 27.2167…; award at most (M1)(M1)(A0).

[3 marks]

b.

Examiners report

[N/A]

a.

[N/A]

b.

Syllabus sections

Topic 3— Geometry and trigonometry » SL 3.2—2d and 3d trig, sine rule, cosine rule, area

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17M.1.SL.TZ1.T_13a:
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18N.2.SL.TZ0.T_5c:
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16N.2.SL.TZ0.T_5b:
the size of angle DAB;
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Find the angle of elevation from B to C.
17M.2.SL.TZ2.T_4b:
Show that angle DBC is 48.7°, correct to three significant figures.
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Show that point $A$ lies outside this circle. Justify your reasoning.
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Show that angle ${\rm{B\hat AE}} = 67.4^\circ$ , correct to one decimal place.
17M.2.SL.TZ2.T_4d:
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16N.2.SL.TZ0.T_5a:
the length of BD;
19M.2.SL.TZ2.T_2d:
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Find the area of the region ABCD.
16N.1.SL.TZ0.T_11a:
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19M.1.SL.TZ1.T_10a:
Find the size, in degrees, of angle BÂC.
18M.2.SL.TZ1.T_1e:
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17M.2.SL.TZ1.T_2d:
Find the length of the perimeter of ABCDE.
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Show that the size of angle BÂC is 20.2°, correct to 3 significant figures.
18M.2.SL.TZ2.T_5a.i:
Use Giovanni’s diagram to show that angle ABC, the angle at which the Tower is leaning relative to the
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18M.2.SL.TZ2.T_5a.ii:
Use Giovanni's diagram to calculate the length of AX.
18M.2.SL.TZ2.T_5a.iii:
Use Giovanni's diagram to find the length of BX, the horizontal displacement of the Tower.
18M.2.SL.TZ2.T_5b:
Find the percentage error on Giovanni’s diagram.
17N.2.SL.TZ0.T_3a:
Show that ${\text{BD}} = 93{\text{ m}}$ correct to the nearest metre.
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Calculate angle ${\rm{B\hat CD}}$ .
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Calculate Abdallah’s estimate for the area.
17N.2.SL.TZ0.T_3d.ii:
Find the percentage error in Abdallah’s estimate.
19M.2.SL.TZ1.T_2a:
Find the length ${\text{AB}}$ , giving your answer to four significant figures.
19M.2.SL.TZ1.T_2b:
Find the total area of the two rectangles that make up the roof.
19M.2.SL.TZ1.T_2d:
Find the percentage error in her estimate.
19M.2.SL.TZ1.T_2e:
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State whether this new arrangement will allow Olivia to fit more solar panels to the roof. Justify your answer.
19M.2.SL.TZ2.T_2a:
Find the distance from A to C.
19M.2.SL.TZ2.T_2b.i:
Find the size of angle ${\text{B}}\mathop {\text{A}}\limits^ \wedge {\text{C}}$ .
19M.2.SL.TZ2.T_2b.ii:
Find the size of angle ${\text{C}}\mathop {\text{A}}\limits^ \wedge {\text{D}}$ .
19M.2.SL.TZ2.T_2c:
Find the size of angle ${\text{A}}\mathop {\text{C}}\limits^ \wedge {\text{D}}$ .
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Calculate the area of triangle EAD.
18M.2.SL.TZ1.T_1b:
Calculate the total volume of the barn.
18M.2.SL.TZ1.T_1f:
Calculate the total length of metal required for one support.
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Show that the equation in part (a)(i) simplifies to $3{x^2} + 19x - 414 = 0$ .
17M.2.SL.TZ1.T_2b:
Find the length of CD.
17M.2.SL.TZ1.T_2e:
Calculate the length of CF.
18N.2.SL.TZ0.T_5d:
A vertical pole, TB, is constructed at point B and has height 25 m.

Calculate the angle of elevation of T from, M, the midpoint of the side AC.
17M.2.SL.TZ2.T_4a:
Find the length of the path BD.
17M.2.SL.TZ2.T_4c:
Find the area of the park.
16N.2.SL.TZ0.T_5c:
the area of triangle ABD;
16N.2.SL.TZ0.T_5e:
the length of AP;
20N.2.SL.TZ0.T_3a:
Calculate the length of $BD$ .
20N.2.SL.TZ0.T_3c:
Calculate the area of triangle $BDC$ .

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Topic 3— Geometry and trigonometry