when the plan had flown 4,150 feet from the airport where it had taken off, it had covered a horizontal distance of 3,360 feet. what is the angle at which the plane rose from the ground to the nearest degree?

Question

jim_thompson5910 · Answer

if you do the drawing, you'll get something like this

|dw:1427580922688:dw|

jim_thompson5910 · Answer

A = airport
P = plane

jim_thompson5910 · Answer

does that make sense?

anonymous · Answer

yes so what would i do next

jim_thompson5910 · Answer

in reference to angle x, we have the adjacent and hypotenuse as the known sides
|dw:1427581068287:dw|

jim_thompson5910 · Answer

which trig function uses adjacent and hypotenuse together?

anonymous · Answer

cos

jim_thompson5910 · Answer

yep

jim_thompson5910 · Answer

cos(angle) = adjacent/hypotenuse

cos(x) = 3360/4150

jim_thompson5910 · Answer

what is the next step to isolating x?

anonymous · Answer

divide the 3360 by 4150?

jim_thompson5910 · Answer

what do you get

anonymous · Answer

0.80963855421

jim_thompson5910 · Answer

so if cos(x) = 0.8096 roughly, then what is the approximate value of x?

anonymous · Answer

would i plug that number in for x

jim_thompson5910 · Answer

no

jim_thompson5910 · Answer

have you learned about inverse cosine? or arccosine?

anonymous · Answer

like a year ago i basically forget it all! and this is a worksheet i am trying to help my little brother with

jim_thompson5910 · Answer

the idea of the inverse cosine is to undo cosine

so for example, if you plug in x = 1 into cos(x), you'll get some number as a result
then if you take that same number and plug it into arccos(x), you'll get the result of 1 back. So the arccos takes you back to the original input

jim_thompson5910 · Answer

cos(x) = 0.8096

arccos( cos(x) ) = arccos(0.8096) ... apply arccos to both sides

x = arccos(0.8096)

x = ??

wolf1728 · Answer

Basically, if the cosine of 10 degrees = 0.98481
Then the arc cosine of 0.98481 = 10 degrees
(Hope I'm not confusing things by tossing in this extra information).

jim_thompson5910 · Answer

I'm taking advantage of the rule arccos(cos(x)) = x

where x is some angle in degrees such that $\Large 0 < x < 90$

anonymous · Answer

i got 0.99 which i still dont think is correct

jim_thompson5910 · Answer

what kind of calculator do you have?

anonymous · Answer

its a scientific calculator i just think i plugging in numbers in the wrong places

jim_thompson5910 · Answer

do you have an arccos function on it? or a $\large \cos^{-1}$ button?

anonymous · Answer

cos-1

jim_thompson5910 · Answer

push the $\large \cos^{-1}$ then type in 0.8096 and hit enter

anonymous · Answer

i got  35.9 which would round to 36

jim_thompson5910 · Answer

yep 36 degrees roughly

anonymous · Answer

okay thank you for all the help

jim_thompson5910 · Answer

you're welcome