How would I do this one?
From a balloon 760 feet high, the angle of depression to the ranger headquarters is 89°18'. How far is the headquarters from a point on the ground directly below the balloon (to the nearest foot)?

Question

How would I do this one?
From a balloon 760 feet high, the angle of depression to the ranger headquarters is 89°18'. How far is the headquarters from a point on the ground directly below the balloon (to the nearest foot)?

anonymous · Answer

@jim_thompson5910

jim_thompson5910 · Answer

What answer did you get?

anonymous · Answer

These were the choices..
-1 ft 
4 ft 
7 ft 
9 ft 
But I don't know how to work this one. It would be wanted in degrees.. Right?

jim_thompson5910 · Answer

Hint: see this attached image

anonymous · Answer

That's what I thought.. But you don't do tan(89.3).. THat's normally how I do them, so I'm lost.

jim_thompson5910 · Answer

89°18' = 89 degrees + 18/60 degrees

89°18' = (89 + 18/60) degrees

89°18' = 89.3 degrees

so you are correct there

jim_thompson5910 · Answer

tan(angle) = opp/adj

tan(89.3) = 760/x

solve for x

anonymous · Answer

Oh, okay. Hang on.

anonymous · Answer

I got ~.108. What the poop?

jim_thompson5910 · Answer

tan(89.3) = 760/x

x*tan(89.3) = 760

x = 760/tan(89.3)

x = ??

anonymous · Answer

Oops, I'm an idiot. Lol. I did it backwards. I got 9. C:

jim_thompson5910 · Answer

yep, 9.28561362328544 which rounds to 9

anonymous · Answer

I have one more question that is kind of like this. Do you want me to post it seperately?

jim_thompson5910 · Answer

Either way works

anonymous · Answer

A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed the angle of depression to the boat is 14°52'. When the boat stops, the angle of depression is 45°10'. The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place.

anonymous · Answer

I got 554.88. :)

jim_thompson5910 · Answer

That's very close, but I'm getting something slightly smaller.

anonymous · Answer

How did you do it? I did it the way we did the last problem, and then subtracted my answers. I think my problem strats when I try to convert 14(degrees)52' to all degrees. I got 14.86.

jim_thompson5910 · Answer

Keep it like 14 + 52/60

I typed this into my calculator

200/tan(14+52/60) - 200/tan(45+10/60)

anonymous · Answer

That time I got 554.58.

jim_thompson5910 · Answer

Me too

200/tan(14+52/60) - 200/tan(45+10/60) = 554.579127143252

which rounds to 554.58

anonymous · Answer

Yay! Thank you so much! God bless you! c:

jim_thompson5910 · Answer

you're welcome