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.

Question

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 · Answer

attachment

anonymous · Answer

@jim_thompson5910 @mathstudent55 @dan815 @DanJS

anonymous · Answer

hi

danjs · Answer

hi

danjs · Answer

are you familiar with sin cos and tangent

anonymous · Answer

well im a failure at it

anonymous · Answer

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

danjs · Answer

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

danjs · Answer

which one do you think is the best here?

anonymous · Answer

tangent?

danjs · Answer

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

danjs · Answer

$$\tan(\theta) = \frac{ 49.6 }{ 57.4 }$$

danjs · Answer

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

danjs · Answer

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

anonymous · Answer

yes

danjs · Answer

what you get for the angle theta

anonymous · Answer

wait a sec

anonymous · Answer

darn my calc doesn't do sin cos and tan

danjs · Answer

haha, you prolly should get one for that class

anonymous · Answer

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

danjs · Answer

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

anonymous · Answer

i hav a mac

danjs · Answer

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

danjs · Answer

you understand the trig functions though?

anonymous · Answer

wait arctan of what number?

danjs · Answer

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

anonymous · Answer

it gave me 40.83067315

danjs · Answer

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

danjs · Answer

that is right

anonymous · Answer

what do i do now?

anonymous · Answer

is that the final answer?

danjs · Answer

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

anonymous · Answer

tnx dude u rock

anonymous · Answer

*thnx

anonymous · Answer

:D