Question

an observer standing 40m from a building observes that the angle of elevation of the top and bottom of a flagstaff which is surmounted on the building are 60degree and 45degree respectively. find the height of the tower and the length of the flagstuff

Answer 1

Hope this may help....

Answer 2

$Height \:of \:the \: building (BC) = y\:m$

$Height \:of \:the \: flagstaff (CD) = x \:m$

$Point \: Observer = A$

$Distance \: between \: observer \: to \:base \\of \:the \: building (AB) = 40 \:m$

$i) In \:\triangle ABC ,\\</p><p>tan 45\degree = \frac{BC}{AB}$

$\implies 1 = \frac{y}{40}$

$\implies 40 = y$

$\implies y = 40 \:m \: --(1)$

$i) In \:\triangle ABD,\\</p><p>tan 60\degree = \frac{BD}{AB}$

$\implies \sqrt{3} = \frac{x+y}{40}$

$\implies 40\sqrt{3} = x + 40$

$\implies x = (40\sqrt{3} - 40) \\= 40(\sqrt{3} - 1) \\= 40(1.732 - 1)\\= 40 \times 0.732\\= 29.28 \:m \: --(2)$

Therefore.,

$\red { Height\: of \: the \: building } \green { 40 \: m }$

$\red { Height\: of \: the \: flagstaff } \green { 29.28 \: m }$

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