A 1.6m tall girl stands at a distance of 3.2m from a lampost and casts a shadow of 4.8m on the ground. Find the height of the lampost by using(1)trigonometric ratios(2)property of similar triangles.

Asked by dr.geetanjali.p | 2nd Sep, 2019, 11:29: AM

Expert Answer:

PQ rightwards arrow post
AB rightwards arrow girl
Trigonometric space ratios
in space increment ABR
tanθ equals fraction numerator 1.6 over denominator 4.8 end fraction
in space increment PQR
tanθ equals straight x over 8
so
fraction numerator 1.6 over denominator 4.8 end fraction equals straight x over 8
straight x equals 2.67 space straight m space left parenthesis approx right parenthesis

Similarity
increment PQR tilde increment ABR space... open parentheses AA space test close parentheses
angle straight Q equals angle ABR equals 90 degree
angle straight R space common
so
PQ over QR equals AB over BR... left parenthesis straight c. straight p. straight s. straight t right parenthesis
straight x over 8 equals fraction numerator 1.6 over denominator 4.8 end fraction
straight x equals 2.67 space straight m space left parenthesis approx right parenthesis

Answered by Arun | 2nd Sep, 2019, 04:30: PM

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