Question

HEIGHT OF A KITE Two observers, in the same vertical plane as a kite and at a distance of 30 feet apart, observe the kite at angles of 62 degree and 78 degree, as shown in the following diagram. Find the height of the kite.

Answer 1

$Height \: of \: the \: kite (CD) = h \: feet$

$A \:and \: B \: positions \: of \: two \: observers$

$Distance \: between \: two \: observers (AB)$

$= 30 \:feet$

$Let \: BC = x \: feet$

$i) In \: \triangle ACD ,$

$tan \angle A = \frac{CD}{AC}$

$\implies tan 62\degree = \frac{h}{30+x}$

$\implies 1.881 = \frac{h}{30+x}$

$\implies 1.881(30+x) = h$

$\implies 56.43 + 1.881x= h \: --(1)$

$ii) In \: \triangle BCD ,$

$tan \angle B = \frac{CD}{BC}$

$\implies tan 78\degree = \frac{h}{30+x}$

$\implies 4.705 = \frac{h}{x}$

$\implies 4.705x = h\: ---(2)$

/* From (1) and (2) *)

$4.705x =56.43 + 1.881x$

$\implies 4.705x - 1.881x = 56.53$

$\implies 2.824x = 56.53$

$\implies x = \frac{ 56.53}{2.824}$

$\implies x = 19.98 \:feet$

/* Put x = 19.98 in equation (2) ,we get */

$h = 4.705\times 19.98$

$\implies h = 94\: feet$

Therefore.,

$\red{ Height \:of \: the \:kite } \green { = 94\:feet }$

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