shesolitt
  • shesolitt
As shown below, an observer (O) is located 660 feet from a tree (T). The observer notices a hawk (H) flying at a 35° angle of elevation from his line of sight. What equation and trigonometric function can be used to solve for the height (h) of the hawk? What is the height of the hawk? You must show all work and calculations to receive full credit.
Mathematics
jamiebookeater
  • jamiebookeater
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shesolitt
  • shesolitt
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shesolitt
  • shesolitt
shesolitt
  • shesolitt
plsss help me today lol as in rn i would really love to turn it in asap. im already a fan of you but ill medal you as well.

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More answers

thomas5267
  • thomas5267
Do you remember the trig functions and their definition?
shesolitt
  • shesolitt
yes they relate the angles of a triangle to the lengths of its sides
shesolitt
  • shesolitt
thomas5267
  • thomas5267
Could you name them?
thomas5267
  • thomas5267
And give the definition?
shesolitt
  • shesolitt
right triangle? @thomas5267
shesolitt
  • shesolitt
actually is it sin,cosine and tangent
thomas5267
  • thomas5267
Yes this is a right triangle. It looks like a right triangle and I will assume the tree grow straight lol.
shesolitt
  • shesolitt
lol oksay so what do i do after that @thomas5267
thomas5267
  • thomas5267
One of the trig function can be applied here. The question is which one.
shesolitt
  • shesolitt
one of the trig functions as in sin or cosine or tangent ? @thomas5267
shesolitt
  • shesolitt
im sorry im bad at geo
thomas5267
  • thomas5267
Yes. sin, cos, or tan.
shesolitt
  • shesolitt
how do i know which one it is @thomas5267 lol cus i dont
thomas5267
  • thomas5267
\[ \sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\\ \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\\ \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \]
thomas5267
  • thomas5267
|dw:1444425795313:dw|
thomas5267
  • thomas5267
Hypotenuse is independent of which angle you choose. Adjacent and opposite however do. Note that you cannot choose the right angle to use the trig functions.
thomas5267
  • thomas5267
Hypotenuse is the side that is longest and is opposite to the right angle. Using the opposite to right angle definition is safer since in exams those teachers could trick you and draw a triangle not to scale.
thomas5267
  • thomas5267
|dw:1444425945588:dw|
thomas5267
  • thomas5267
Take a guess?
shesolitt
  • shesolitt
so the function is sin? @thomas5267
shesolitt
  • shesolitt
because it says hypotenuse over opposite
thomas5267
  • thomas5267
Think of what do you have and what do you want.
thomas5267
  • thomas5267
You have the distance to the tree and you want the height of the hawk.
shesolitt
  • shesolitt
im still confused lol im sorry /: @thomas5267
shesolitt
  • shesolitt
so how would i find the hawk do i use the distance formula
shesolitt
  • shesolitt
for the height of the hawk
thomas5267
  • thomas5267
\[\tan(\theta)\] Any ideas?
shesolitt
  • shesolitt
no ): still.. @thomas5267
thomas5267
  • thomas5267
\[ \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\\ (\text{adjacent})\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\text{adjacent}\\ (\text{adjacent})\tan(\theta)=\text{opposite} \]
shesolitt
  • shesolitt
so the function would be tan
shesolitt
  • shesolitt
how do i write an equation @thomas5267
thomas5267
  • thomas5267
\[ \theta=35\deg\\ \text{adjacent}=660\text{ ft} \] All given in the picture.
shesolitt
  • shesolitt
yes that helps lol thanks
shesolitt
  • shesolitt
so for the height i divide 660/35 @thomas5267
thomas5267
  • thomas5267
You want \(660\tan(35\deg)\).
thomas5267
  • thomas5267
|dw:1444427723299:dw|
shesolitt
  • shesolitt
so....an(35)=h660 h=660×tan(35) then i calculate the value of h @thomas5267
thomas5267
  • thomas5267
Yep.
shesolitt
  • shesolitt
thank youuuuu lol i get it now !. so thats all i should write? @thomas5267
thomas5267
  • thomas5267
Yep. You can get \(\tan(35\deg)\) using calculator. Make sure the calculator is using degree mode.
shesolitt
  • shesolitt
i got 0.7 @thomas5267
shesolitt
  • shesolitt
or is it 462.14
shesolitt
  • shesolitt
thats my final answer @thomas5267
thomas5267
  • thomas5267
Yes, but why do you need to state the complementary angle? It is not ask in the question right? \[ \tan(35\deg)=0.7020754 \]
shesolitt
  • shesolitt
thank you soooo muchhhh (:::

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