Find the height of the building.

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]