| Date | None Specimen | Marks available | 7 | Reference code | SPNone.2.sl.TZ0.6 |
| Level | SL only | Paper | 2 | Time zone | TZ0 |
| Command term | Find | Question number | 6 | Adapted from | N/A |
Question
The following diagram shows a pole BT 1.6 m tall on the roof of a vertical building.
The angle of depression from T to a point A on the horizontal ground is \({35^ \circ }\) .
The angle of elevation of the top of the building from A is \({30^ \circ }\) .
Find the height of the building.
Markscheme
METHOD 1
appropriate approach M1
e.g. completed diagram
attempt at set up A1
e.g. correct placement of one angle
\(\tan 30 = \frac{h}{x}\) , \(\tan 35 = \frac{{h + 1.6}}{x}\) A1A1
attempt to set up equation M1
e.g. isolate x
correct equation A1
e.g. \(\frac{h}{{\tan 30}} = \frac{{h + 1.6}}{{\tan 35}}\)
\(h = 7.52\) A1 N3
METHOD 2
\(\sin 30 = \frac{h}{l}\) A1
in triangle ATB, \(\widehat A = {5^ \circ }\) , \(\widehat T = {55^ \circ }\) A1A1
choosing sine rule M1
correct substitution
e.g. \(\frac{{h/\sin 30}}{{\sin 55}} = \frac{{1.6}}{{\sin 5}}\) A1
\(h = \frac{{1.6 \times \sin 30 \times \sin 55}}{{\sin 5}}\) A1
\(h = 7.52\) A1 N3
[7 marks]
