First slide

Applications of trigonometry

Question

A flagstaff stands at the center of a rectangular field whose diagonal is 1200m, and subtends angles $15^{0}$ and $45^{0}$ at the mid points of the sides of the field. The height of the flagstaff is

Moderate

A

200m
B

$300 \sqrt{2 + \sqrt{3}} m$
C

$300 \sqrt{2 - \sqrt{3}} m$
D

400m

Solution

Let OP be the flagstaff of height ‘h’ standing at the center O of the rectangular field ABCD subtending angles $15^{0}$ and $45^{0}$ at E the F, the mid points of the sides AD and DC of the field .
Then $O E = h \cot 15^{0} = h (2 + \sqrt{3})$ and $O F = h \cot 45^{0} = h$
$\Rightarrow E F = h \sqrt{1^{2} + {(2 + \sqrt{3})}^{2}} = 2 h \sqrt{2 + \sqrt{3}}$
$\Rightarrow 1200 = A C = 2 E F = 4 h \sqrt{(2 + \sqrt{3})}$
$\Rightarrow h = \frac{300}{\sqrt{2 + \sqrt{3}}} = 300 \sqrt{2 - \sqrt{3}}$

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