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Date	May 2019	Marks available	2	Reference code	19M.2.SL.TZ2.T_2
Level	Standard Level	Paper	Paper 2	Time zone	Time zone 2
Command term	Find	Question number	T_2	Adapted from	N/A

Question

An archaeological site is to be made accessible for viewing by the public. To do this, archaeologists built two straight paths from point A to point B and from point B to point C as shown in the following diagram. The length of path AB is 185 m, the length of path BC is 250 m, and angle ${\text{A}}\mathop {\text{B}}\limits^ \wedge {\text{C}}$ is 125°.

The archaeologists plan to build two more straight paths, AD and DC. For the paths to go around the site, angle ${\text{B}}\mathop {\text{A}}\limits^ \wedge {\text{D}}$ is to be made equal to 85° and angle ${\text{B}}\mathop {\text{C}}\limits^ \wedge {\text{D}}$ is to be made equal to 70° as shown in the following diagram.

Find the size of angle ${\text{C}}\mathop {\text{A}}\limits^ \wedge {\text{D}}$ .

[1]

b.ii.

Find the size of angle ${\text{A}}\mathop {\text{C}}\limits^ \wedge {\text{D}}$ .

[2]

c.

Markscheme

(CAD =) 53.1° (53.0521…°) (A1)(ft)

Note: Follow through from their part (b)(i) only if working seen.

[1 mark]

b.ii.

(ACD = ) 70° − (180° − 125° − 31.9478°…) (M1)

Note: Award (M1) for subtracting their angle ${\text{A}}\mathop {\text{C}}\limits^ \wedge {\text{B}}$ from 70°.

OR

(ADC =) 360 − (85 + 70 + 125) = 80

(ACD =) 180 − 80 − 53.0521... (M1)

46.9° (46.9478…°) (A1)(ft)(G2)

Note: Follow through from part (b)(i).

[2 marks]

c.

Examiners report

[N/A]

b.ii.

[N/A]

c.

Syllabus sections

Topic 3—Geometry and trigonometry » SL 3.2—2d and 3d trig

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22M.1.SL.TZ1.1:
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22M.1.SL.TZ2.3a:
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22M.1.SL.TZ2.3c:
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22M.1.SL.TZ1.2b:
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17N.1.SL.TZ0.T_10c:
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19M.1.SL.TZ1.T_8a:
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17M.2.SL.TZ1.T_2a.i:
Write down an equation for the area of ABCDE using the above information.
18M.2.SL.TZ1.T_1d:
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18M.2.SL.TZ2.S_2b:
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18M.2.SL.TZ1.T_1e:
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19N.2.SL.TZ0.T_2b:
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19N.2.SL.TZ0.T_5d:
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19N.2.SL.TZ0.T_2a:
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19N.2.SL.TZ0.T_2d:
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SPM.1.SL.TZ0.14b:
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17M.2.SL.TZ1.T_2d:
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16N.2.SL.TZ0.T_5c:
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16N.2.SL.TZ0.T_5b:
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21M.2.SL.TZ1.2a:
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16N.2.SL.TZ0.T_5d:
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16N.2.SL.TZ0.T_5e:
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21M.2.SL.TZ2.2b:
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19M.2.AHL.TZ2.H_1:
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17M.2.SL.TZ1.T_2c:
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19N.2.SL.TZ0.T_2f:
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20N.2.SL.TZ0.T_3a:
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EXN.1.SL.TZ0.11a:
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EXN.1.SL.TZ0.11b:
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Find $BD$ . Fully justify any assumptions you make.
21M.1.SL.TZ2.9a:
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21M.1.SL.TZ1.9:
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21M.1.SL.TZ2.9b:
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21M.2.SL.TZ2.2a:
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21M.2.SL.TZ2.5a:
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21N.1.AHL.TZ0.11:
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He wants the enclosure to take up as little of the current field as possible.

Find the minimum possible area of the triangular enclosure $ABC$ .
21N.2.SL.TZ0.4a:
Find the angle of depression from $M$ to $N$ .
21N.2.SL.TZ0.4b.i:
Find $CV$ .
21N.2.SL.TZ0.4c:
By finding an appropriate value, determine whether Joshua is correct.
21N.2.SL.TZ0.4d:
To avoid water leaking into the ground, the five interior sides of the reservoir have been painted with a watertight material.

Find the area that was painted.
21N.1.SL.TZ0.2a:
Calculate the value of $θ$ , the measure of angle $MŜB$ .

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Topic 3—Geometry and trigonometry