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.

- shesolitt

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- shesolitt

##### 1 Attachment

- shesolitt

@thomas5267

- 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

Do you remember the trig functions and their definition?

- shesolitt

yes they relate the angles of a triangle to the lengths of its sides

- shesolitt

@thomas5267

- thomas5267

Could you name them?

- thomas5267

And give the definition?

- shesolitt

right triangle? @thomas5267

- shesolitt

actually is it sin,cosine and tangent

- thomas5267

Yes this is a right triangle. It looks like a right triangle and I will assume the tree grow straight lol.

- shesolitt

lol oksay so what do i do after that @thomas5267

- thomas5267

One of the trig function can be applied here. The question is which one.

- shesolitt

one of the trig functions as in sin or cosine or tangent ? @thomas5267

- shesolitt

im sorry im bad at geo

- thomas5267

Yes. sin, cos, or tan.

- shesolitt

how do i know which one it is @thomas5267 lol cus i dont

- thomas5267

\[
\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\\
\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\\
\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}
\]

- thomas5267

|dw:1444425795313:dw|

- 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

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

|dw:1444425945588:dw|

- thomas5267

Take a guess?

- shesolitt

so the function is sin? @thomas5267

- shesolitt

because it says hypotenuse over opposite

- thomas5267

Think of what do you have and what do you want.

- thomas5267

You have the distance to the tree and you want the height of the hawk.

- shesolitt

im still confused lol im sorry /: @thomas5267

- shesolitt

so how would i find the hawk do i use the distance formula

- shesolitt

for the height of the hawk

- thomas5267

\[\tan(\theta)\]
Any ideas?

- shesolitt

no ): still.. @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

so the function would be tan

- shesolitt

how do i write an equation @thomas5267

- thomas5267

\[
\theta=35\deg\\
\text{adjacent}=660\text{ ft}
\]
All given in the picture.

- shesolitt

yes that helps lol thanks

- shesolitt

so for the height i divide 660/35 @thomas5267

- thomas5267

You want \(660\tan(35\deg)\).

- thomas5267

|dw:1444427723299:dw|

- shesolitt

so....an(35)=h660
h=660×tan(35)
then i calculate the value of h @thomas5267

- thomas5267

Yep.

- shesolitt

thank youuuuu lol i get it now !. so thats all i should write? @thomas5267

- thomas5267

Yep. You can get \(\tan(35\deg)\) using calculator. Make sure the calculator is using degree mode.

- shesolitt

i got 0.7 @thomas5267

- shesolitt

or is it 462.14

- shesolitt

thats my final answer @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

thank you soooo muchhhh (:::

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