Two birds sit at the top of two different trees 57.4 feet away from one another. The distance between the second bird and a bird watcher on the ground is 49.6 feet.
What is the angle measure, or angle of depression, between the first bird and the bird watcher?
Two trees that are 49 point 6 feet tall with a bird on top of each. Distance between the birds is 57 point 4 feet. Angle of depression between birdwatcher and first bird is unknown.

- anonymous

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- anonymous

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- anonymous

@jim_thompson5910 @mathstudent55 @dan815 @DanJS

- anonymous

hi

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## More answers

- DanJS

hi

- DanJS

are you familiar with sin cos and tangent

- anonymous

well im a failure at it

- anonymous

i know the 3 but im bad at the formulas and calculating

- DanJS

sin = opp/hyp
cos = adjacent / hypotenuse
tan = opposite / adjacent

- DanJS

which one do you think is the best here?

- anonymous

tangent?

- DanJS

yes. the tangent of an angle in a right triangle is the ratio of the side opposite that angle over the adjacent side

- DanJS

\[\tan(\theta) = \frac{ 49.6 }{ 57.4 }\]

- DanJS

\[\tan^{-1}[\tan(\theta)] = \theta =\tan^{-1}\frac{ 49.6 }{ 57.4 }\]

- DanJS

you can use a calculator right? make sure it is in degree mode, not radians

- anonymous

yes

- DanJS

what you get for the angle theta

- anonymous

wait a sec

- anonymous

darn my calc doesn't do sin cos and tan

- DanJS

haha, you prolly should get one for that class

- anonymous

yea my mom said she's gonna buy me a 80$ calc just for math

- DanJS

just open the windows calculator in accessories and put into scientific modeq

- anonymous

i hav a mac

- DanJS

ok well it is just calculator work, you would take the arctangent of that number, it is near 40 degrees

- DanJS

you understand the trig functions though?

- anonymous

wait arctan of what number?

- DanJS

the tangent is the opposite side the angle over the hypotenuse, then i just took the arctangent of both sides

- anonymous

it gave me 40.83067315

- DanJS

\[\tan^{-1}[\tan(\theta)] = \theta =\tan^{-1}\frac{ 49.6 }{ 57.4 } \approx 40~degrees\]

- DanJS

that is right

- anonymous

what do i do now?

- anonymous

is that the final answer?

- DanJS

i have to run sorry, look up tangent and arctangent, the anser is what you said... gl

- anonymous

tnx dude u rock

- anonymous

*thnx

- anonymous

:D

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