A boy, 1.4 metres tall standing at the edge of a river bank sees the top of a tree on the edge of the other bank at an elevation of 55 $^{o}$ . Standing back by 3 metres, he sees it at an elevation of 45 $^{o}$ .
(a) Draw a rough figure showing these facts.
(b) How wide is the river and how tall is the tree?
$[sin 5 5^{o} = 0.8192, cos 5 5^{o} = 0.5736, tan 5 5^{o} = 1.4281]$

Question

A boy, 1.4 metres tall standing at the edge of a river bank sees the top of a tree on the edge of the other bank at an elevation of 55

^{o}

. Standing back by 3 metres, he sees it at an elevation of 45

^{o}

.
(a) Draw a rough figure showing these facts.
(b) How wide is the river and how tall is the tree?

[sin 5 5^{o} = 0.8192, cos 5 5^{o} = 0.5736, tan 5 5^{o} = 1.4281]

Filo · Accepted Answer

The rough sketch is as followsBF represents the tree, DG is the first position of the boy and AE is the new position.CD represents the river.We have : AE = DGLet DC = x, then EC = (x + 3) m.tan45o=ECCF​⇒1=x+3CF​⇒CF=x+3    ...... (i)tan55o=DCCF​⇒1.4281=xCF​⇒CF=1.4281×x       ..... (ii)From (i) and (ii), we have1.4281x=x+30.4281x=3⇒x=0.42813​∼7mWidth of the river = CD = 7 mHeight of the tree = BF = BC = CF = (1.4 + 7 + 3)m = 11.4 m

Question Text	A boy, 1.4 metres tall standing at the edge of a river bank sees the top of a tree on the edge of the other bank at an elevation of 55 $^{o}$ . Standing back by 3 metres, he sees it at an elevation of 45 $^{o}$ . (a) Draw a rough figure showing these facts. (b) How wide is the river and how tall is the tree? $[sin 5 5^{o} = 0.8192, cos 5 5^{o} = 0.5736, tan 5 5^{o} = 1.4281]$
Answer Type	Text solution:1
Upvotes	151

Text solutionVerified

Practice questions from similar books