Question

1. A circus artist is climbing a 20 m long rope, which is
tightly stretched and tied from the top of a vertical
pole to the ground. Find the height of the pole, if
the angle made by the rope with the ground level is
30° (see Fig. 9.11).​

Answer 1

Step-by-step explanation:

HEY MATE..........

$let \: the \: height \: of \: the \: pole \: ab \\ \\ assuming \\ \\ \: that \: rope \: is \: tied \: at \:p oint \: c \: \\ \\ it \: is \: given \: that \: \\ \\ lenth \: of \: rope \: = 20 |m| \\ \\ hence \: \\ ac = 20 |m | \\ \\ also \: angle \: made \: by \: rope \: \\ \\ with \: the \: ground \: level \: is \: 30 \: degree \\ \\ hence \: < acb = 30 \: degree \\ \\ we \: need \\ \\ \: to \: find \: height \: of \: pole \: i.e. \: ab \\ \\ since \: the \: pole \: is \: vertical \: \\ \\ < abc = 90 \: degree \: \\ \\ in \: right \: triangle \: abc \\ \\ sin(c) = \frac{side \: opposite \: to \: angle \: c}{hypotenuse \: } \\ \\ \sin(30) = \frac{ab}{ac} \\ \\ \frac{1}{2} = \frac{ab}{20} \\ \\ \frac{1}{2} \times 20 = ab \\ \\ 10 = ab \\ \\ \\ \\ hence \: height \: of \: pole \: = 10 |m|$

HOPE IT HELPS YOU

Answer 2

Step-by-step explanation:

$\mathfrak{ \huge{ \green{ \underline{given}}}} \\ \mathfrak{ \large{ \red{ac \: = \: 20 \: m}}} \\ \mathfrak{ \large{ \red{angle \: of \: elevation = {30}^{o}}}} \\ \mathfrak{ \huge{ \green{ \underline{to \: find}}}} \\ \mathfrak{ \large{ \red{height \: of \: pole \: (h) \: = \: ?}}} \\ \mathfrak{ \huge{ \green{ \underline{formula \: to \: be \: used}}}} \\ \mathfrak{ \large{ \red{sin \: θ \: = \: \frac{perpendicular}{hypotenuse} }}} \\ \mathfrak{ \large{ \red{ \sin \: {30}^{o} \: = \: \frac{1}{2} }}} \\ \mathfrak{ \huge{ \green{ \underline{solution}}}} \\ \mathfrak{ \large{ \blue{sin \: θ \: = \: \frac{perpendiular}{hypotenuse} }}} \\ \mathfrak{ \large{ \blue{ \sin \: c \: = \: \frac{ab}{ac} }}} \\ \mathfrak{ \large{ \blue{ \sin \: {30}^{o} \: = \: \frac{ab}{20} }}} \\ \mathfrak{ \large{ \blue{ \frac{1}{2} \: = \: \frac{ab}{20} }}} \\ \mathfrak{ \large{ \blue{ab \: = \: \frac{20}{2} }}} \\ \mathfrak{ \large{ \blue{ab \: = \: 10}}} \\ \mathfrak{ \large{ \orange{ \underline{ => height \: of \: pole \: = \: 10 \: m}}}}$