A 1 6m tall, girl stands ata distance of 3 2m from a lamp-post and cats a shadow of 4 - Maths - Some Applications of Trigonometry

Question

A 1 6m tall, girl stands ata distance of 3 2m from a lamp-post
and cats a shadow of 4 8m on the grond Find the height of the
lamp-post by using (i)trignometric ratios (ii)property of similiar
triangles

Lalit Mehra · Accepted Answer

Dear Student!

Let AB be the tower of height h m Suppose CD be the height of the girl and DE be the length of shadow of the girl Given, CD = 1 6 m, AD = 3 2 cm and DE = 4 8 m In Î”CDE, $\tan E = \frac{CD}{DE} (\tan θ = \frac{Perpendicular}{Base}) ∴ \tan E = \frac{1 6 m}{4 8 m} = \frac{1}{3} (1)$ In Î”BAE, $\tan E = \frac{AB}{AE} ∴ \frac{1}{3} = \frac{h m}{(3 2 m + 4 8 m)} (U \sin g (1)) \Rightarrow \frac{1}{3} = \frac{h}{8} \Rightarrow h = \frac{8}{3}$ Thus, the length of the lamp post is $\frac{8}{3} m$ Method 2: In Î”CDE and Î”BAE, âˆ CED = âˆ BEA (Common) âˆ CDE = âˆ BAE (90Âº) âˆ´ Î”CDE âˆ¼ Î”BAE (AA similarity criterion) $\Rightarrow \frac{CD}{AB} = \frac{CE}{BE} = \frac{DE}{AE} (Corresponding sides are proportional) \Rightarrow \frac{1 6 m}{AB} = \frac{4 8 m}{(3 2 m + 4 8 m)} \Rightarrow \frac{1 6 m}{AB} = \frac{4 8 m}{8 m} \Rightarrow AB = \frac{1 6 m \times 8 m}{4 8 m} = \frac{8}{3} m$ Thus, the length of the lamp post is $\frac{8}{3} m$ Cheers!

A 1.6m tall, girl stands ata distance of 3.2m from a lamp-post and cats a shadow of 4.8m on the grond. Find the height of the lamp-post by using (i)trignometric ratios (ii)property of similiar triangles.