Question

the angle of elevation from a point on the ground to the top of the tower id 36 degrees 6 minutes. the angle of elevation from a point 192 feet farther back is 27 degrees 32 minutes. find the height of the tower. round answer to nearest hundredth.

Answer 1

this the diagram see what can we get from this

Answer 2

im looking for the height of the tower

Answer 3

i'm lagging ...

Answer 4

that the height of the tower i called h

Answer 5

oh I see

Answer 6

x is 140?

Answer 7

I used tangent ratio with tan 36.1=x/192

Answer 8

hmm how did you use it

Answer 9

tan36.1 =x/192 x=192tan(36.1) x=192(0.729)

Answer 10

we have two equation involving tan
\[\Large \begin {cases} \tan(27^{\circ}32')=\frac{h}{x}\\ \tan (36^{\circ}6')=\frac{h}{x+192}\end{cases}\]

Answer 11

of course you need to convert those angle measure to only degree first

Answer 12

just remember that 60 min = 1 rotation = 360 degrees

Answer 13

or just 30 min = 180 degrees

Answer 14

idfk?

Answer 15

just do \[27 + 32/60\]

Answer 16

and the same for the other one

Answer 17

sorry the net is bad, i'm lagging

Answer 18

36 + 6/60
the result will be in degrees only

Answer 19

after that solve using the two equations

Answer 20

I already know 36 degrees 6 minutes is 36.1 and 27 degrees is 27.53 what next

Answer 21

next is to evaluate tan of those angles

Answer 22

\[0.52=\frac{h}{x}\]
\[0.73=\frac{h}{x+192}\]

Answer 23

solve for x in the first equation
then replace what you found into the second equation
this is basic system of two equations

Answer 24

\[x=\frac{h}{0.52} \Longrightarrow 0.73=\frac{h}{\frac{h}{0.52}+192}\]