An observer (O) spots a plane flying at a 35° angle to his horizontal line of sight. If the plane is flying at an altitude of 17,000 ft., what is the distance (x) from the plane (P) to the observer (O)?

Question

anonymous · Answer

20,757 feet
24,251 feet
29,639 feet
31,262 feet

anonymous · Answer

I'm assuming you are working in a little trigonometry section? I can help if so

anonymous · Answer

yes I am

anonymous · Answer

ok great one sec, let me draw out a little diagram

anonymous · Answer

okay thank you!!

anonymous · Answer

|dw:1394405972374:dw|

anonymous · Answer

To add on to my diagram, we are actually trying to find the hypotenuse of this triangle so we can use the angle we are given, and the altitude we are given to set up the sine of 35 degrees.

sin35 = opposite(altitude)/hypotenuse(x)
sin35 = 17,000/hypotenuse
17,000 time (sin35) = hypotenuse(x)
So now we use our calculator to fin sin35 and multiply it by 17,000 and then you have x!

anonymous · Answer

Would you like me to solve for X completely with my scientific calculator or are you good from here? @mathhelpxx

jdoe0001 · Answer

$\bf sin(\textit{observer's angle})=\cfrac{\textit{altitude}}{x}\implies \textit{altitude}\cdot sin(\textit{observer's angle})=x$

anonymous · Answer

I got 9750 but i think its wrong @ChanHamm

jdoe0001 · Answer

ahemmm wait a sec... shoot $\bf sin(\textit{observer's angle})=\cfrac{\textit{altitude}}{x}\implies x=\cfrac{\textit{altitude}}{sin(\textit{observer's angle})}$

anonymous · Answer

Let me check one second

anonymous · Answer

That is correct!

anonymous · Answer

But thats not an option

jdoe0001 · Answer

hmmm the hypotenuse will be longer than either side
if one side is 17,000, the hypotenuse is surely more than that

anonymous · Answer

Ok lets take a look at that I think we actually need to divide 17,000 by the sin35

jdoe0001 · Answer

$\bf sin(\textit{observer's angle})=\cfrac{\textit{altitude}}{x}\implies x=\cfrac{\textit{altitude}}{sin(\textit{observer's angle})}$
   notice ChanHamm 's picture

anonymous · Answer

@jdoe0001 was correct I sort of messed up explaning x = altitude/ sin35

anonymous · Answer

so would it be .00003374?

anonymous · Answer

try this, 17,000 divided by the sin35

anonymous · Answer

I got your third answer choice doing that

anonymous · Answer

29638?

anonymous · Answer

Yes! Good Job

anonymous · Answer

oh I had to round it i see!

anonymous · Answer

can you help me with another?

anonymous · Answer

Yes, it would be much easier if you opened it in a new question. DO you mind

anonymous · Answer

sure!

anonymous · Answer

:)