Question

An observer (O) is located 500 feet from a school (S). The observer notices a bird (B) flying at a 39° angle of elevation from his line of sight. What equation and trigonometric function can be used to solve for the height (h) of the bird? What is the height of the bird? Pick another trigonometric function and describe why that function is not appropriate when trying to solve for (h). You must show all work and calculations to receive full credit.

Answer 1

@saifoo.khan can you please help me with this question?

Answer 2

Do you know the trigonometric ratios?

Answer 3

yes

Answer 4

Which ratio contains opposite and adjacent of the angle?

Answer 5

tangent?

Answer 6

am i correct?

Answer 7

Yes. Try applying.

Answer 8

tan (39) = OB/OS?

Answer 9

Correct.

Answer 10

okay :) so what do i do next?

Answer 11

Insert the value of OS and solve for OB.

Answer 12

how can i do that? can you plz help me? or at least give hints?

Answer 13

OS is 500.

Answer 14

And BS is h.

Answer 15

so what do u want me to do now?

Answer 16

so u want me to say tan (39) = x/y x for OB and y for OS?

Answer 17

tan(39) = h/500

h is what we have to find.

Answer 18

oh ok now u want me to get h by itself?

Answer 19

h = 500 tan(39)

Answer 20

exactly so that'll be the final answer?

Answer 21

Use a calc to solve.

Answer 22

okay give me on sec @saifoo.khan

Answer 23

I got h = 404.892

Answer 24

Correct

Answer 25

that's all i had to do?

Answer 26

Yes.

Answer 27

can you please help me put everything we said together in complete sentences?

Answer 28

@saifoo.khan

Answer 29

Refer to the calculations using Mathematica 9.

Answer 30

but i need help putting all the work shown here together in complete sentences

Answer 31

can you please help anyone? @tHe_FiZiCx99 @robtobey

Answer 32

@saifoo.khan

Answer 33

From the sketch provided, the bird's height is 500 times the tangent of 39 degrees.

500 times the secant of 39 degrees yields the length of the slant range between the observer and the bird and not the bird's height.

Answer 34

doesn't sound like anything we just did nvm. i'll get help from @saifoo.khan

Answer 35

@shinebrightlikeadimon : he's doing it right.
Just try to elaborate things and write it here. And we will correct you if wrong.

Answer 36

okay i will :) thanks and also ramadan mubarak lol

Answer 37

@shinebrightlikeadimon

I think we are making a mountain out of a mole hole here.

Answer 38

Haha. Kher Mubarak. #iftaaaaaarrriii

Answer 39

hahaha yep! lol idk what to write for this one pick another trigonometric function and describe why that function is not appropriate when trying to solve for (h). can you please help? @saifoo.khan

Answer 40

Pick another function. Like let's say sin.
And then tell why you can't use the sin function here.

Answer 41

hahah cute story.. idk why xD

Answer 42

Lol.

Answer 43

HELP! lol

Answer 44

TRY!

Answer 45

i can't i dont know stuff about sin and cos i just learned about all this.

Answer 46

Sine ratio? Cos ratio? No?

Answer 47

yes

Answer 48

sine = opposite/hypotenuse and cosine = adjacent/hypotenuse

Answer 49

Can you use sin instead of tan?

Answer 50

no

Answer 51

Why?

Answer 52

cuz sine u find for opposite and hypotenuse but for tangent u find for opposite and adjacent?? i'm just guessing

Answer 53

Do you know the value of hypotenuse?

Answer 54

no

Answer 55

Then how can use sin?

Answer 56

i'm soooo confused!!

Answer 57

just telll me whyy and i'll remember why

Answer 58

When you use the ratios, you MUST know two values to find the third one.

Like in the case of tan, you had 39 and 500 AND you had to find the third one.

So now, when using sin/cos, you know the angle, but you don't know the hypotenuse to find h.
\[\sin39 = \frac{h}{hypotenuse}, \cos39 = \frac{500}{hypotenuse}\]
In sin, you don't know both.
In cos, there's no h which is your gial.

Answer 59

goal*

Answer 60

ohhhhh okaaayyy i did not know that thank you so much!

Answer 61

can u check my work with the complete senteces and why we cant use different trigonometric ratios?

Answer 62

To find the height of the bird i had to use to trigonometric ratio tangent to solve for it which in this case is: tan (39) = OB/OS and now we plug in everything that's given to us and get tan (39) = h/500 and h is what we have to find. Now, we have to get h by itself and it'll look like h = 500 tan (39), and h = 404.892

Answer 63

Right.

Answer 64

and then i just have to add how different functions wouldn't work?

Answer 65

@saifoo.khan

Answer 66

Yes.

Answer 67

thank you so much! you;re really good. Will u be able to help me with 4 more at least?

Answer 68

About to leave. #EshanNamaz

Answer 69

oohhh okay haha one last question when you said in sin u dont know both? what did u mean by that? whats both?

Answer 70

@saifoo.khan

Answer 71

sin = opp/hyp

By both I meant, the value opposite and the value of hypotenuse.

Answer 72

ohh okkk! jazakallah