Question

A man standing 22m away from the foot of tree, sees the top of the tree at an elevation of 50°. Find the height of the tree.

( sin50=0.766, cos50=0.64, tan50= 1.192)

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Answer 1

Answer:

The rough sketch is as follows

BF represents the tree, DG is the first position of the boy and AE is the new position.

CD represents the river.

We have : AE = DG

Let DC = x, then EC = (x + 3) m.

tan45

o

=

EC

CF

⇒1=x+3

CF

⇒CF=x+3 ...... (i)

tan55

o

=

DC

CF

⇒1.4281=

x

CF

⇒CF=1.4281×x ..... (ii)

From (i) and (ii), we have

1.4281x=x+3

0.4281x=3⇒x=

0.4281

3

∼7m

Width of the river = CD = 7 m

Height of the tree = BF = BC = CF = (1.4 + 7 + 3)m = 11.4 m

solution