Question

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.

Answer 1

@thomas5267

Answer 2

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.

Answer 3

Do you remember the trig functions and their definition?

Answer 4

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

Answer 5

@thomas5267

Answer 6

Could you name them?

Answer 7

And give the definition?

Answer 8

right triangle? @thomas5267

Answer 9

actually is it sin,cosine and tangent

Answer 10

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

Answer 11

lol oksay so what do i do after that @thomas5267

Answer 12

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

Answer 13

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

Answer 14

im sorry im bad at geo

Answer 15

Yes. sin, cos, or tan.

Answer 16

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

Answer 17

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

Answer 18

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.

Answer 19

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.

Answer 20

Take a guess?

Answer 21

so the function is sin? @thomas5267

Answer 22

because it says hypotenuse over opposite

Answer 23

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

Answer 24

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

Answer 25

im still confused lol im sorry /: @thomas5267

Answer 26

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

Answer 27

for the height of the hawk

Answer 28

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

Answer 29

no ): still.. @thomas5267

Answer 30

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

Answer 31

so the function would be tan

Answer 32

how do i write an equation @thomas5267

Answer 33

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

Answer 34

yes that helps lol thanks

Answer 35

so for the height i divide 660/35 @thomas5267

Answer 36

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