The angle of depression from the top of the tree to the tip of the shadow is 25°. Find the height of the tree to the nearest tenth.
a.
16.8 feet
b.
18.2 feet
c.
23.4 feet
d.
39.7 feet

- anonymous

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- anonymous

##### 1 Attachment

- anonymous

##### 1 Attachment

- freckles

|dw:1437363564659:dw|
just use the tangent ratio

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## More answers

- freckles

though that is the angle of elevation not angle of depression

- anonymous

how do i solve it what equation

- freckles

alpha is the angle of elevation which is 25 deg
recall tan is opp divided by adjacent

- anonymous

which one is adjacent

- freckles

since it does say angle of depression
I wonder if it is talking about this angle being 25 deg|dw:1437363976910:dw|

- freckles

|dw:1437364051842:dw|
but that still makes that one angle 25 deg

- anonymous

so what do i divide by

- freckles

so it didn't matter

- freckles

you just
do
\[\tan(25)=\frac{\text{ opp side of the angle with measurement } 25 \deg}{ \text{ adj side of the angle with measurement } 25 \deg}\]

- freckles

the opp side is what I called h in the picture

- freckles

anyways let me know if you need further help

- anonymous

i dont know what the measurement is

- freckles

which one?

- anonymous

h

- freckles

h is what you are solving for

- freckles

remember h is the height of the tree

- freckles

that is what you are solving the equation for

- freckles

you are given the adjacent side
the side that touches the angle (and no adjacent side is not the hyp)

- freckles

|dw:1437364301549:dw|

- anonymous

so what next

- freckles

pluggin those numbers into equation I gave

- freckles

then just solving it for h
and then bingo you are done

- triciaal

use the equation given above by @freckles

- freckles

\[\tan(25)=\frac{\text{ opp side of the angle with measurement } 25 \deg}{ \text{ adj side of the angle with measurement } 25 \deg} \\ \tan(25)=\frac{h}{36}\]
notice I just put what I called the opp where I said opp side
notice I just put what I called the adjacent measurement for the adjacent side
can you solve the equation?

- triciaal

|dw:1437364501206:dw|

- triciaal

did you get A?

- anonymous

i didnt get anything yet

- anonymous

what i got 900. i know that isnt right

- freckles

ok @GEOMETRYHELP10011 do you know how to do tan(25) in your calculator ?

- anonymous

no

- freckles

oh that could be a big problem for solving the equation

- freckles

because it does require you to type tan(25) in your calculator

- freckles

you should see a button with tan on it

- freckles

you should see it next to things like sin and cos

- freckles

if you can't find them tell me the name of your calculator
and I can tell you where it is

- anonymous

i got at 16.7

- freckles

ok that's great

- freckles

that is what I and @triciaal also got

- freckles

well 16.8

- triciaal

to round to the nearest tenth solve to 2 decimals you have 16.78 then look at the 2nd place if 5 or more add 1 to the digit before 8 is more than 5 so you round to 16.8
if the 2nd digit was less than 5 then you would drop it and round to 16.7

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