Question

a man observes the top of a building 52m high situated in front of him and finds the angle of elevation to be 30degree . if the distance between man and building is 86m find height of the men

Answer 1

$\bf{Hope \; it \; helps \; you ~☆}$

Answer 2

Answer:

2.347 m

Used: tan30° = 1/√3. and √3 = 1.732

Step-by-step explanation:

$\bold{ \red{Given:}} \\ \bold{Height \: of \: building \: 52m, } \\ \bold{angle \: of \: elevation \: 30° \: and \: distance \: between \: man \: and \: building \: is \: 86m.} \\ \bold{ \red{Refer \: to \: the \: attachment:}} \\ \bold{ AE = height \: of \: building \: = \: 52m} \\ \bold{CD= BE = height \: of \: man \: h(supposed)} \\ \bold{and \: DE = BC = distance \: between \: man \: building = 86m} \\ \bold{and \:∠ACB = 30° } \\ \bold {\underline{In \: ΔABC, }} \\ \bold{tan∠ACB = tan30° = \frac{AB}{BC} = \frac{AB}{86}.} \\ \\ \bold{ \implies{ \frac{1}{ \sqrt{3} } =\frac{AB}{86}. }} \\ \\ \bold{ \implies{AB = \frac{86}{ \sqrt{3} } .}} \\ \\ \bold{ \red{Take: \: \sqrt{3 } = 1.732 }} \\ \bold{ \implies{AB = 49.652 }} \\ \bold{ \red{Since, \: BE + AB = AE}} \\ \bold{ \implies{BE + 49.652 = 52}} \\ \bold{ \implies{BE = 52 - 49.652 }} \\ \bold{ \implies{ \underline{BE(h) = 2.347m}}} \\ \green{ \bold{Therefore ,\: (h)height \: of \: man \: is \: 2.347m.}}$