A tree and a flag pole are on the same horizontal ground, A bird on top of the tree observes the top and bottom of this flag pole below it at angle 45 degrees and 60 degrees respectively, If the tree is 10.65 meters high ,calculate and correct to 3 significance figures the hieght of the flag pole

Answer 1

did you make your sketch?
On mine I labeled the top of the pole as P and it bottom as Q.
I marked the bird on the tree as A
Draw a horizontal from A to meet PQ at R
let PR = x, then PQ = 10.65+x

In triangle ARQ
tan60° = 10.65/AR
AR = 10.65/tan60

Triangle ARP is right-angled, and
tan45° = x/AR
x = AR tan45, but we know tan 45 = 1
so x = AR
= appr 6.1458..

height of pole = 10.65 + 6.1458
= 16.8 m high, correct to 3 significant figures.

Answer 2

Umm.. sorry Reiny
but your final answer is wrong
you are meant to subtract the answers not add them

the tree is higher than the flagpole

Answer 3

Exactly