Question

A phone company worker needs to know the height of a cell tower, so he decides to use a 2 m pole and shadows cast by the sun, as shown in the diagram. Both shadows end at point B. What is the height of the tower? (Points : 5) 30 m 32 m 36 m 40 m

Answer 1

2 is to 3; as h is to (45+3)

Answer 2

what? @antonio_xx2

Answer 3

similar triangles have similar ratios

Answer 4

@mrgenius

Answer 5

can u explain this to her @ash2326

Answer 6

@maguihajji I will draw the figure here, so that we can understand the question.
C is the cell tower, P is the pole of height 2 meters.

Do you follow this?

Answer 7

yeah

Answer 8

Ok let's make this a triangle, so that we use properties of triangle

So we have big triangle ADEB

Answer 9

and small triangle PEB. Do you follow this

Answer 10

yeah

Answer 11

ok if we look at angles CDB and PEB, can you tell me their value in degrees?

Answer 12

omg i dont know are they a right triangle what is happening

Answer 13

yes, you are right. they are straight and therefore right angles.

So we can
angle CDB= angle PEB.

Now look closely at angle DBC and EBP, can you find the relation b/w them?

Answer 14

ummm i dont know they share the same angle?

Answer 15

Yes the two triangles have a common angle and therefore equal angles.

Recall that we already have two angles as right angles therefore equal

What can you tell me about the third angle of both the triangles

Answer 16

its equal too?

Answer 17

You check and confirm

Answer 18

what? check?how? im so confused jesus

Answer 19

it's easy, recall that sum of angles of a triangle is 180

Answer 20

so for both triangles sum will be equal
180=180
we can also write 180 in term of sum of all three
90+Angle1+ Angle 3= 90+ Angle 1 + Angle 3
now angle 1 is same for both already which is the common angle
so third angle for both will be?

Answer 21

ummmm 45........?

Answer 22

I just want to know the relation between third angle of both the triangles not the value

Answer 23

but what does that have to do with the tower?

Answer 24

if we know the relation between angles, then only we can apply formula to find the height of tower.
It's like if you don't know if a rectangle is square, how you can find its area if you have only one side given???

Answer 25

omg im so confused right now

Answer 26

oh ok, I will make it clear. We have this
180= 180

Answer 27

LEFT side 180 degrees I will write as sum of angles of bigger triangle and right side as sum of smaller triangle

Answer 28

\[\angle DAB+\angle ABD+\angle BDA=\angle EPB +\angle PBE+\angle BEP\]

We know
\[\angle BDA=\angle BEP=90\]
so
\[\angle DAB+\angle ABD+90=\angle EPB +\angle PBE+90\]
do you follow till now?

Answer 29

i think so

Answer 30

and
\[\angle ABD= \angle PBE\]
so
we are left with
\[\angle DAB+\angle ABD+90=\angle EPB +\angle PBE+90\]
Let's cancel the common terms
\[\angle DAB+\cancel {\angle ABD}+\cancel {\cancel {90}}=\angle EPB +\cancel{\angle PBE}+\cancel {\cancel{90}}\]
so the third angles of both the triangles are equal

Answer 31

so what does that mean? whats the answer

Answer 32

We will be able to find the answer now. So the two triangles are similar.
that means their sides are in same ratio so
\[\frac{AD}{PE}=\frac{DB}{EB}\]
where AD is height of tower also/

Do you follow?

Answer 33

i do follow however i dont know how to do ratios

Answer 34

I will help with ratios. Can you look in the diagram and tell the values of PE, DB, EB

Answer 35

pe - 2
db - 48?
eb- 3?

Answer 36

is the answer 32?

Answer 37

Good, you are right. Let's plugin these values in the formula.
\[\frac{AD}{PE}=\frac{DB}{EB}\]

\[\frac{AD}{2}=\frac{48}{3}\]

Answer 38

yes, you are right, how did you find?

Answer 39

i cross multiplied omg thank you so so so so so so so so sooooo muchhh <3 life saver

Answer 40

You're welcome, did you understand the solution?

Answer 41

sure

Answer 42

solve it using Pythogoras theorem, i guess you have got the solution by now. Sorry couldnt be on